Talk:Schrödinger equation/Archive 2

Lagrangean??
Paranoidhuman (talk) 10:29, 14 May 2010 (UTC)


 * Well, it is


 * $$\mathcal{L}\left(\psi, \mathbf{\nabla}\psi, \dot{\psi}\right) = \mathrm i\hbar\, \frac{1}{2} (\psi^{*}\dot{\psi}-\dot{\psi^{*}}\psi) - \frac{\hbar^2}{2m} \mathbf{\nabla}\psi^{*}  \mathbf{\nabla}\psi - V( \mathbf{r},t)\,\psi^{*}\psi$$


 * Maybe one should add it, true... —Preceding unsigned comment added by 212.186.99.222 (talk) 20:53, 13 November 2010 (UTC)

Schrödinger Group?
I have seen mentions in the literature of the Schrödinger group in an increasing number of contexts (aging situations, potentials in AdS). I think the article would benefit from some discussion of the group, but I do not know enough about to author a section. —Preceding unsigned comment added by 128.173.125.74 (talk) 15:33, 13 October 2009 (UTC)

mistake
shouldnt the formula where kinetic energy + potential have hbar squared instead of hbar? —Preceding unsigned comment added by 62.136.133.147 (talk) 13:57, 17 May 2008 (UTC)

SE in spherical symmetric potential
Dan Gluck added a subsection to this article making a few spelling mistakes, which Pfalstad corrected. However, there are also a few minor flaws in the content, e.g., particle mass μ of the electron. No electron was mentioned earlier and mass is indicated by M. Before I (or somebody else) correct(s) these minor things, I like to know whether we all agree that this article is the place for Dan's addition. In the list of analytic solutions we find two articles that treat the spherical symmetric problem. If Dan is not satisfied with these two articles, maybe he should improve those. To me Dan's addition seems fairly arbitrary, he could have added to the present article any solution from the list of analytic solutions. Any comments?--P.wormer 15:24, 22 May 2007 (UTC)


 * I removed the section, and merged it with particle in a spherically symmetric potential since the additions seem to fit better there. --HappyCamper 16:13, 25 May 2007 (UTC)


 * Sorry for my speling :-) mistakes, but that's the price English speakers have to pay for their language being the international one. Anyway the merging seems fine to me. Dan Gluck 14:29, 12 June 2007 (UTC)

GA Article?
As a professor in physics from Denmark, I am very disappointed, I am concerned because the English written articles have a tendency to penetrate into all other languages. This article has so many errors/misunderstanding that a GA-status will harm the Wikipedia. Quantum mechanics do not need to be presented as something very complicated, and the use of the Dirac's notation is throughout the article completely wrong. Sincerely j.h.povlsen 80.163.26.74 00:36, 13 August 2007 (UTC)


 * I reacted here on this comment.--P.wormer 12:32, 13 August 2007 (UTC)

And I emphasize again, that this article does not present the work of Schroedinger, The same article could as well have been about the equations of Heisenberg. The article starts in it's very first equation with a misinterpretation of the Dirac notation, and then it goes on by describing a Complex Hilbert Space. Let me you remind, that Schroedinger was not aware of any of the above mentioned complexities about the world. He was a physicist, and his equation did not just jump out from nothing! He thought, without a thought on Hilbert space, but on the "quantum mechanics" as he knew it at that time. And the quantum mechanics was the discoveries from Planck, Bohr, Luis de Broglie and Einstein. The Planck/Einstein discovery was, that the energy quantization of light/(Electro-magnetic waves) could be expressed as
 * $$E=\hbar \omega$$

while Luis de Broglie discovered a relation between momentum and wavelength
 * $$p=\hbar k$$, where k is the wavenumber, and p the momentum.

In connection with that the energy, according to Newton, consists of a kinetic part and potential part as in
 * $$E=\frac{p^2}{2m}+V$$

he looked at a monochromatic wave $$\exp(i(kx- \omega t))$$, and realized that the energy could be evaluated as an eigenvalue to
 * $$ E<-> i\hbar\frac{\partial}{\partial t}$$

and a momentum component $$p_{x}$$, similarly could be derived as an eigenvalue to
 * $$ p_{x}<->-i\hbar\frac{\partial}{\partial x}$$

And by inserting this into the Newton energy rule he reached his named equation:
 * $$i\hbar\frac{\partial}{\partial t}\psi=[-\frac{\hbar^2}{2m}\nabla^2+V]\psi$$

which (in Wikipedia) sadly, seems to become an untold story. I hope some one, some day will tell it. Sincirely j.h.povlsen 80.163.26.74 04:40, 15 August 2007 (UTC)
 * Thank you, j.h.povlsen, you are correct. The article is unnecessarily opaque.  Schroedinger's original derivation couldn't have used Dirac's notation (obviously!); instead it followed directly on from de Broglie's work the year before.
 * Perhaps the article should have a section entitled "Schroedinger's derivation" or something. --Michael C. Price talk 06:20, 15 August 2007 (UTC)
 * I have added a new "History and development" section. Perhaps some of the details of the next section could be reduced. --Michael C. Price talk 12:51, 15 August 2007 (UTC)


 * Thank you Michael for taking me serious! I know that I some times can seem arrogant!
 * I still dislike the section Mathematical Formulation, and think it should be omitted.A new section Physical interpretation of the wave function might be an idea? And I also find that the section The Time independent Scrodinger equation has to many (trivial) details, mixed up with a far to "complicated mathematical terminology" and suggest that the section should be reduced and divided into subsections. I would prefer a much stronger focus on the physical implications, without any use the Dirach notation. For instance a discussion on the discrete spectrum and the continuous spectrum. Below I have rewritten The Time independent Scrodinger equation (which now is far to short!!) and also suggested a new section, on the relation to the classical mechanics (here we could also include the Virial thorem).

The Time independent Scrodinger equation
We can find stationary solutions to the Schrodinger by looking at solutions separable in time and space as:$$ \psi\left(x,y,z,t\right)=\phi\left(x,y,z\right)g\left(t\right)$$ which inserted into the time dependent Schoedinger equation reveal solutions on the form $$\psi\left(x,y,z,t\right)=\phi\left(x,y,z\right)\exp\left(-i\frac{E}{\hbar}t\right)$$ with the time independent part being an eigenfunction to:
 * $$ \left[-\frac{\bigtriangledown^{2}}{2m}+V\left(x\right)\right]\phi\left(x,y,z\right)=E\phi\left(x,y,z\right)$$

where $$E$$ is interpreted as the energy. This equation can be analytically solved for a number of very physical important cases such as the Coulomb potential (orbitals in the hydrogen atom), and the harmonic oscillator (lowest order approximation of arbitrary potential functions $$V\left(x,y,z\right)$$ around a minimum). "

Connection with classical mechanics
The quantum mechanics need in a proper formulation to include the classical mechanics in it's macroscopic limit, and the Shroedinger equation does indeed that, as realized by Ehrenfest. Ehrenfest showed from the time dependent Schroedinger equation that the the expectation value $$\left\langle A\right\rangle $$, defined as



\left\langle A\right\rangle \equiv\frac{\int\int\int\left(\psi^{*}A\psi\right)dxdydz}{\int\int\int\left(\psi^{*}\psi\right)dxdydz}$$ of a pysical operator $$A$$ (i.e. a Hermetian operator) evolves in time as



\frac{\partial}{\partial t}\left\langle A\right\rangle =\frac{i}{\hbar}\left\langle \left[A;H\right]\right\rangle $$ where $$H$$, the Hamiltonian is $$\left[-\frac{\bigtriangledown^{2}}{2m}+V\left(x\right)\right]$$ and $$\left[A;H\right]$$ denotes the commutator defined as

\left[A;H\right]=AH-HA$$ and by considering the posiotion operator $$\overrightarrow{r}=\left(x,y,z\right)$$ and the momentum operator $$\overrightarrow{p}=\left(p_{x},p_{y},p_{z}\right)$$ he derived the correspondance equations

\frac{d}{dt}\left\langle \overrightarrow{r}\right\rangle  =  \frac{\left\langle \overrightarrow{p}\right\rangle }{m}$$


 * $$ \frac{d}{dt}\left\langle \overrightarrow{p}\right\rangle  =  -\left\langle \overrightarrow{\bigtriangledown}V\right\rangle$$

In agreement with Newtons second law.

Sincirely 80.163.26.74 00:01, 17 August 2007 (UTC)j.h.povlsen
 * Thanks --I'm glad you liked it (I thought you would).
 * I agree we could probably lose the entire "Mathematical Formulation" section (and trim the other sections), but I'd rather not delete it immediately -- let's wait for a consensus to develop one way or the other.
 * I don't see the need for a classical limit section here, since it is not part of Schroedinger's work (certainly not his equation), but more Ehrenfest's, which why it is explained at Ehrenfest theorem and classical limit.--Michael C. Price talk 03:06, 17 August 2007 (UTC)

Problem with "Historical background and development" section
From artical and similarly since: 1:$$ \frac{\partial}{\partial x} \psi = i k_x \psi $$ then 2:$$ p_x \psi = \hbar k_x \psi = -i\hbar\frac{\partial}{\partial x} \psi $$ and hence 3:$$ p_x^2 \psi = -\hbar^2\frac{\partial^2}{\partial x^2} \psi $$ I agree with formula 1 and 2 as currently derived however I derive a different answer for formula 3:
 * $$ p_x^2 \psi = p_x p_x \psi = p_x \cdot -i\hbar\frac{\partial}{\partial x} \psi = \hbar k_x \cdot -i\hbar\frac{\partial}{\partial x} \psi =

\hbar \frac{\frac{\partial}{\partial x} \psi}{i \psi} \cdot -i\hbar\frac{\partial}{\partial x} \psi = \frac{-\hbar^2\left (\frac{\partial}{\partial x} \psi\right )^2}{\psi} \overset{\underset{\mathrm{?}}{}}{\ne} -\hbar^2\frac{\partial^2}{\partial x^2} \psi$$
 * $$\because k_x=\frac{\frac{\partial}{\partial x} \psi}{i \psi}

\land \frac{\partial}{\partial x} \psi\cdot\frac{\partial}{\partial x} \psi = \left (\frac{\partial}{\partial x} \psi\right )^2 \overset{\underset{\mathrm{?}}{}}{\ne} \frac{\partial^2}{\partial x^2} \psi$$ So how does this get accounted for? (the problem points are denoted $$\overset{\underset{\mathrm{?}}{}}{\ne}$$)--ANONYMOUS COWARD0xC0DE 23:51, 4 September 2007 (UTC)
 * The formula are valid for the plane wave solution. More complex solutions are built up by superposition / fourier analysis. --Michael C. Price talk 06:32, 5 September 2007 (UTC)


 * No information regarding the problem was conveyed to me in those two sentences. Please respond to my problem in particular.  --ANONYMOUS COWARD0xC0DE 22:19, 5 September 2007 (UTC)
 * In the plane wave example $$p_x = \hbar k_x$$ is not a function of x.


 * Hence
 * $$ p_x^2 \psi = p_x (\hbar k_x \psi) = \hbar k_x (p_x \psi) =(\hbar k_x)^2 \psi = (-i\hbar\frac{\partial }{\partial x})^2 \psi = -\hbar^2\frac{\partial^2}{\partial x^2} \psi$$
 * and hence:
 * $$ p_x^2 \psi = -\hbar^2\frac{\partial^2}{\partial x^2} \psi $$
 * --Michael C. Price talk 09:18, 7 November 2007 (UTC)


 * How do you get from the square of the first derivative to the second derivative? This appears to be nonsense, or else is using some further theory which ought to be explained.Mbays (talk) 18:20, 29 November 2008 (UTC)


 * He's using the theory of Fourier transforms. If you have a sinusoid, like sin(kx), then taking a derivative multiplies by k, and taking two derivatives multiplies by k^2. So that multiplying by k squared is the same as taking two derivatives. This has absolutely no relation to the nonlinear operation of squaring the first derivative. It would be too much of a digression to explain Fourier stuff here, but there is a free standing article on it.Likebox (talk) 18:36, 29 November 2008 (UTC)


 * Ah, sorry, yes. It is fine, but the derivation is slightly confusing. I have changed it slightly to a hopefully clearer version - please review.Mbays (talk) 19:15, 29 November 2008 (UTC)

Unheadered stuff at the top
Someone should go back through this article and change the sloppy notation for the wavefunction Psi. Psi is a function of x and t, while psi is one a function of x. This can wildly confuse a physicist or student looking for mathemetical expressions described by the Schrodinger Equation. Perhaps putting the wavefunction in the form of its variables Psi(x,t) and psi(x) can alleviate this confusion. —Preceding unsigned comment added by GaiaMind (talk • contribs) 05:29, 28 October 2007 (UTC)

Removed "one dimensional"
Referring to the state vector as "one dimensional" is misleading; it is typically infinite dimensional Peter1c 07:29, 7 November 2007 (UTC)

Delisted from GA
In order to uphold the quality of Good articles, all articles listed as Good articles are being reviewed against the GA criteria as part of the GA project quality task force. While all the hard work that has gone into this article is appreciated, unfortunately, as of February 15, 2008, this article fails to satisfy the criteria, as detailed below. For that reason, the article has been delisted from WP:GA. However, if improvements are made bringing the article up to standards, the article may be nominated at WP:GAN. If you feel this decision has been made in error, you may seek remediation at WP:GAR. I've had to delist this article from GA status as part of the good article quality control sweeps. It lacks inline references which became a good article requirement in 2006, possibly after this article was passed. I've listed this article at our unreferenced good article task force. Once adequate inline sources have been added, hopefully the article can easily reattain GA status. --jwandersTalk 12:26, 15 February 2008 (UTC)

My sandbox version
I am in the process of cleaning up the article via my sandbox version. Feel free to comment on it. Thanks. MP (talk•contribs) 12:14, 17 February 2008 (UTC)

Rewrite (old)
Upon request, I've just rewritten the article with my sandbox version. A lot more work still needs to be done though. MP (talk•contribs) 17:09, 8 March 2008 (UTC)
 * Great. Hopefully many hands will make light work. --Michael C. Price talk 17:51, 8 March 2008 (UTC)

Removal of huge chunk of text
I decided to remove the subsections Schrodinger wave equation and wave function as I think there is no point in repeating what's already been said in the article and a lot of the stuff will not help to actually understand the Schrodinger equation per se. Hope this is ok; comments/criticisms welcome. Thanks. MP (talk•contribs) 06:53, 14 March 2008 (UTC)
 * OK with me. --Michael C. Price talk 09:39, 14 March 2008 (UTC)

Notation
I've always seen the time-dependent wavefunction written with a capital psi and the time-independent function with a lowercase one, e.g. $$\Psi(\mathbf{x},t) = \psi(\mathbf{x}) e^{-iEt/\hbar}$$. It took me a moment to work out what the article was talking about as a result. Is there a particular notation used by most physicists, or was my physics textbook just using an unconventional convention (so to speak)? &mdash; Xaonon (Talk) 19:37, 27 March 2008 (UTC)

This article
Is it really necessary to add 'citation needed' 3-4 times per sentence? It's unreadable. Put a sentence in the beginning to give a conceptual (useless) description, then give the math for people who want to know. To paraphrase Lord Kelvin, if you cannot quantify it, you don't know what you're talking about. —Preceding unsigned comment added by 70.249.215.163 (talk) 22:58, 27 March 2008 (UTC)

too complex
this article is too complex to be comprehended by general public. this article presume the reader to have an advanced understading and knowledge in the subject. a less mathematical approach, a more conceptual approach is required for people who have limited knowledge in physics and mathematics. I suggests to remove the more complex parts from this page into a new article. So that it would be possible for general reader to understand this subject. —The preceding unsigned comment was added by 202.152.240.246 (talk) 15:22, 2 May 2007 (UTC).


 * Why should every Wikipedia article be for the general reader (and who is the "general reader": College graduate? High school graduate with science or without science? High school dropout?) This article starts with a reference to the article Introduction to quantum mechanics that is meant to be as easy as is possible for an abstract subject as quantum mechanics. Read this if you really want to know something about the Schrödinger equation and you lack the mathematical background. It is useless to keep on starting new articles because somebody out there takes him/herself as the absolute standard of comprehension. Personally, I skip articles about Kantian philosophy and such things, but if philosophers add advanced articles about it, I applaud it. It will make Wikipedia the better for it. Nobody forces me to read these articles, but they are there if I ever develop an interest in Immanuel Kant. The computer disks are patient, specialized articles are in nobody's way and hurt nobody. If you don't understand them, ignore them.--P.wormer 16:03, 2 May 2007 (UTC)


 * You make a good point that leads me to illustrate a general rule you seem to suggest. Let me repeat your question - who is the "general reader"? Indeed, the only thing we may presuppose about a reader of this article is that they are interested in the subject matter of the page in question. They either searched directly for the article, or followed a link from a related stub. Who knows what level of scientific or mathematical understanding they possess? In fact, we cannot really be assured that they have a basic level of English literacy. Some concepts are unable to be presented in a completely lowest-common-denominator fashion. Since we cannot make any assumptions about the reader, we ought to engage the subject on _the_terms_of_the_subject_, in absence of a clearly defined target audience. There exists a direct link at the top of the article to an introductory article outlining some of the basic concepts of QM, and that really ought to be enough. It makes no sense to attempt to simplify the subject, especially when much of it is in the realm of multivariable function math, with a variety of very specific structures which are already as condensed and fundamental as they can be expressed. Any attempt to simplify this page will only lead to confusion. In fact, I find the page to be lacking in specific definition of the particular constraints wherein S.E. is discussed. I would like to see a more technically apt page, that begins by discussing S.E. at a more general level, rather than the specific constraints applied to this page (which appears to be aimed at the particular problem of solving S.E. under assumed constraints on the _actual_ original works). Not that I pretend to be an expert on the matter, QM is considerably difficult both in concept and mathematical construction. So, although I don't believe in _simplifying_ the article, I do support the expansion of the article to give a clearer definition that is both More General in context, and which provides more detailed explanations of some of the mathematical constructs used. I admit my own contributions need reworking by an expert in the field. Wernhervonbraun (talk) 11:57, 24 April 2008 (UTC)


 * I agree with the original poster, in that the article is almost unbearably esoteric. When I read through most of the higher science articles, I see two possible outcomes. Either the reader already knows everything in the article, or the reader cannot understand the article. In very few complex science articles can I see a reader having a basic knowledge of a subject, and using the information presented in the article to gain a better understanding of the topic. It just won't happen. Wikipedia isn't a place to show off your newfound language skills, it's an informational resource. Utilizing the most complex language available to describe subjects which can be expressed better makes it a poor informational resource. —Preceding unsigned comment added by 69.209.126.57 (talk) 02:12, 10 September 2009 (UTC)


 * Apologies but I must defend the people who write the more esoteric articles here. When you examine something like quantum mechanics/tunneling/the schrodinger equation, if you care to read the bits that are not math you are provided with a very convenient set of analogies and resources that can give you a qualitative picture, though it may not be complete. As for the mathematical rigor of many of these articles, the entirety of the necessary knowledge to understand this article is already present on wikipedia and even more thoroughly documented on wikibooks and the veritable wikiverse that exists outside this domain. Saying the article is too esoteric out of hand without actually clicking the many references it makes to the necessary background information via one or multiple jumps makes you one of three things: lazy, daft, or merely annoying. The only danger these articles have is the potential to spread already widely held misconceptions. But then again, if you were in it for more than just a tertiary overview or memory jog, you wouldn't be here right now. —Preceding unsigned comment added by 129.21.69.216 (talk) 10:41, 10 August 2010 (UTC)

Microscopic particles
I dissagree with the wording that an electron is a microscopic paricle, its smaller than that! Noosentaal (talk) 17:53, 7 April 2008 (UTC)

Historical Accuracy
I think that one should not present pseudo-history as history. It is possible to give modern mathematical derivations, but in a historical discussion I think it is good to stick to the actual events, if not the exact formulas.Likebox (talk) 02:44, 15 May 2008 (UTC)


 * I don't know what you're referring to, but the previous heuristic derivation is now as clear as mud. --Michael C. Price talk 19:03, 16 May 2008 (UTC)


 * "Modern psuedo-history" is very important in science pedagogy. Yes, it should not be misrepresented as actual-history, but it hasn't been here, so no worries. A "modern derivation" is not possible because, strictly, it is impossible to theoretically "derive" any new theory. Actual-history is also not very useful for a variety of reasons: different language/notation; correct conclusions chanced upon despite incorrect reasoning; different context of thought. Cesiumfrog (talk) —Preceding comment was added at 03:24, 31 May 2008 (UTC)


 * If it really were impossible to derive new theories from older ones by reasoning, there would have been no new theories developed in the 20th century. Almost everything after electrodynamics, including the Schrodinger equation, was derived with scarcely any experimental input, and certainly none which suggested the mathematical form which the theory should take. A derivation in physics is not the same as a derivation in mathematics--- it does not produce a new theory from axioms. Rather, it tries to reconcile new domains of experience with known limits where old thoeries are known to work. More often than not, there is a unique plausible solution, and the mathematical form of a new theory is determined from the old theory plus the qualitative insights about the physics of the new domain. This is what the word derivation means in physics, and this is the derivation that is the type of derivation which is the subject of this discussion.


 * I also disagree about the usefulness of pseudo-history. I think that representing history falsely is often a justification for propagating historical myths--- like deutsche physic or the modern idea that everything is done by Americans, the way I see it, and leaves some brilliant and massively influential scientists without a shred of recognition.Likebox (talk) 05:57, 27 June 2008 (UTC)

Pedagogical Note
Too much detail is just as bad as too little. The person who is reading this page should be able to reproduce elementary algebraic manipulations.Likebox (talk) 21:58, 15 May 2008 (UTC)
 * I don't know what you're referring to, but the previous heuristic derivation is now as clear as mud. --Michael C. Price talk 19:03, 16 May 2008 (UTC)


 * Is it? I'll try to fix it. Maybe I don't have the knack.Likebox (talk) 20:13, 16 May 2008 (UTC)
 * My problem with the longer "derivation" is that much of the material is irrelevant to the derivation. We don't have to know about Hamiltonian's equations or conservation of momentum or the "short-wave limit" in order to derive Schrodindger's equation from the classical E = KE + PE.  What are described are attributes or properties of the SE which should be described else where in the article.--Michael C. Price talk 16:50, 18 May 2008 (UTC)


 * As I commented below, you are absolutely right on this if the goal is only to justify the mathematical form of the equation, and you might even be right from a pedagogical point of view. But I wanted to make it clear, from a physical point of view, that when Schrodinger sat down to find his equation, he wasn't faced with a problem that had too few constraints, it was the exact opposite. Students, I think, have the impression that it's like a guessing game, where there's a lot of freedom to choose. But the requirement that Hamilton's equations come out right for wavepackets is so strong that there is more information there than what is strictly necessary to get at the form of the equation, and the rest of the stuff is a consistency check which allows you to be sure that it is correct as physics. If Hamilton's equations weren't just so, there would have been no wave equation. Of course, the modern point of view on this is the other way around--- that classical mechanics has a Hamiltonian description ultimately because quantum mechanics is there underneath. Anyway, I hope you feel the article is improved. Cheers.Likebox (talk) 21:13, 18 May 2008 (UTC)


 * The reason that I edited the heuristic derivation is because I remembered some of my confusions when I was learning this: The original derivation substituted operators for the energy and momentum for plane waves where it is obvious, and then made it seem clear that the potential will just add to the kinetic energy. This is best justified by the short-wavelength limit, where wavepackets have sharp trajectories with the k changing from place to place as the wavepacket moves while the frequency stays fixed. It takes a little thinking to see that this produces wavepacket trajectories which have the right acceleration.


 * What does not take much effort is to see that wavepackets have the classical velocity, or that the energy is conserved. In one dimension, if you have a wavepacket moving with the classical velocity and and you know that the total energy is conserved, it follows that the acceleration is the classically correct one, since the change in momentum is determined by the change in the potential.


 * but in two dimensions or three, only the change in the magnitude of the momentum is guaranteed to come out right from energy conservation. To see that the wavepackets change direction correctly according to the classical force requires thinking about the way in which wavefronts shift about when the wavenumber is slowly varying.Likebox (talk) 21:51, 16 May 2008 (UTC)
 * Do you have any objection the to heuristic derivation being restored alongside the current reworked version? --Michael C. Price talk 12:27, 17 May 2008 (UTC)


 * I undid most of the reworking, so that it goes more like it did before. If you still hate it, by all means restore the original. But I found a way to make a nice quick way to argue the second of Hamilton's equations.Likebox (talk) 20:25, 17 May 2008 (UTC)


 * Ok, maybe it's no good, but give it a chance before you revert, because the earlier discussion was both a little verbose and misrepresented Schrodinger's contribution.Likebox (talk) 20:48, 17 May 2008 (UTC)
 * I'm not going to revert your additions, but I still think there is a place for the original heuristic derivation in the article that someone without a physics degree will have a chance of following. BTW the claim that Schroedinger accepted the CI is incorrect.--Michael C. Price talk 11:40, 18 May 2008 (UTC)

(deindent) Maybe you're right, I am not so great with psychology. But I think that the previous argument was essentially identical, except it was done with more detail to make the algebraic steps more explicit. The issue I had with that (and I might be psychologically totally off base here) is that I think it makes the reader lose the forest for the trees. It had many equations whose only purpose was to restate the equivalence of E and \omega and p and k. By doing this, a larger fraction of the "steps" are easier to follow, but only because the number of steps is made larger by including more algebraic restatements of p=hk. So, it would say "p=hk" and later "k=i d/dx \psi" and later "p=i\hbar d/dx". This sort of thing bothered me when I was a student (At least I think I remember that it did) because it would obscure the essentially new insights--- in this case the substitution of derivative operators in the energy equation--- by hiding them among a list of algebraic manipulations which should be internalized by the reader first, before doing anything else. But perhaps its the exact opposite. Maybe if there are more familiar identities, there is a feeling of familiarity which aids the process of understanding.

The group-velocity stuff might be an unnecessary hurdle for a first read, and it might need to be removed. You might also be right that a careful restatement of p=hk multiple times will reinforce understanding, because different people might "click" on different restatements. I have no confidence that the current version is any good at all. The previous presentation might be significantly better. Probably this is best figured out by asking some students who have just finished learning quantum mechanics.

About Schrodinger and Copenhagen--- I read conflicting stuff on this. Everybody agrees that at first, he hated the Copenhagen interpretation, and thought \psi was a physical charge density or something, but after Born's paper he (and Einstein and everyone else) came to agree that, given the formalism, a statistical interpretation is the only sensible one. The question that remains is whether he held out hope that this was a statistical approximation to an underlying determinisic DeBroglie-Bohm theory, or if he had some Wigneresque proto-Everettist ideas. This I don't know for sure. In the new Einstein biography by Isaacson, the author states that Schrodinger was sympathetic to Einstein's view at least up to EPR, but in the 1940s goes on a rant to someone or other about how Einstein was a stupid old man when it came to quantum mechanics. That's why I assumed he had come to accept that the Copenhagen interpretation is correct. If you have better information, please fix it. I don't have any insight into Schrodinger's thinking.Likebox (talk) 20:14, 18 May 2008 (UTC)


 * I noticed you put back the old discussion--- that's a good solution. Let the reader have a choice. I would put the reference to Isaacson for Schrodinger, but it's not really conclusive at all.Likebox (talk) 20:52, 18 May 2008 (UTC)

"Schrödinger tried unsuccessfully to interpret it as a charge density." This is a very interesting claim! In the history of relativistic QM, it is well known that the Klein-Gordon equation was originally discarded because its wavefunction failed to fit the probability interpretation. BUT! In modern QFT, the Klein-Gordon equation is actually correct -- the wavefunction just has to be interpreted as charge density rather than probability. So if Schroedinger really started out interpreting the wavefunction as charge density, and considering that he also preceded Klein and Gordon by trying that equation before trying the one he is now known for, surely there is more interesting history worth telling here (or at least, the Klein-Gordon page needs a better history section). Cesiumfrog (talk) 05:01, 31 May 2008 (UTC)

Full Copenhagen vs. Statistical interpretation
There is a difference between believing that the Copenhagen interpretation is incorrect or incomplete and believing that the statistical interpretation of the wavefunction is incorrect. While I don't know for sure whether Schrodinger believed that the Copenhagen interpretation was a final statement on the nature of physical reality, I am sure that, like Einstein and everybody else, he accepted Born's analysis as correct and realized that the wavefunction could only be interpreted as a probability. This was a universal conclusion, everyone agreed with Born's interpretation. For example, Einstein is directly quoted in Isaacson as saying that the only possible interpretation of the wavefunction is statistical, that this is an unavoidable conclusion. This was (and still is) such a clear fact that I can't imagine Schrodinger rejected it. He certainly understood, although I'm sure with distaste, that the probability is proportional to the wavefunction squared (although perhaps with a philosophy radically different than those that were codified by Bohr). His often quoted dislike of quantum discontinuities should be properly read as a sign that he initially wanted to avoid all quantum jumps with a continuous wave formalism, but failed. I don't have any insight into whether he thought that quantum mechanics was a statistical approximation to a deeper underlying theory.Likebox (talk) 00:17, 20 May 2008 (UTC)
 * You may be sure that Schrodinger "accepted Born's analysis as correct and realized that the wavefunction could only be interpreted as a probability." but I am not; in fact I'm sure he didn't. Can you find a statement by S to that effect? --Michael C. Price talk 03:22, 20 May 2008 (UTC)
 * Honestly, if you are not I am not so sure anymore--- since I am pretty sure that you've probably read as much about it as I have. But please verify it, because I am sure that Einstein accepted Born's interpretation, and Schrodinger and Einstein were pretty much on the same page. The reason I am sure about Einstein is Isaacson's biography.Likebox (talk) 07:51, 20 May 2008 (UTC)
 * I do see the distinction you're making between Born's probability amplitude and the CI (although note that Born was a committed CIist)). And I know Einstein accepted that Born's probability amplitude was empirically correct to mid 20th C levels of measurement.  However I'm not so sure that Schrodinger went along with this (although, as you say, Einstein and Schrodinger normally agreed on such matters).  I've got Moore's bio of S so I'll double-check.--Michael C. Price talk 08:42, 20 May 2008 (UTC)
 * Thanks for clearing that up.Likebox (talk) 21:45, 22 May 2008 (UTC)

Article gone mad
This article has undergone a major sequence of changes, the second last (before my revert) of which (by an anon.) completely obliterated crucial info. on the forms of the Schrodinger equation, but kept a mass of mathematical detail that is not relevant to the article or point being made at hand. I intend to sort out this article at some point. There is too much maths which could - and should - be moved to articles dealing with those issues more directly. MP (talk•contribs) 18:44, 13 June 2008 (UTC)


 * I did the madness--- so much craziness takes a while, so I was autologged out. The "crucial info" which I deleted was a sequence of mathematical boxes and associated prose which in my opinion said nothing. It was box after box of purely formal symbol manipulation with no physical or mathematical content. Meaningless formalism drives away readers. In order to reinsert it, it should be accompanied by a concrete problem, a mathematical formulation or a physical system, otherwise it is only some contributors pet philosophy. That's my opinion.Likebox (talk) 20:38, 13 June 2008 (UTC)


 * Since my contribution was essentially negative--- I deleted a bunch of stuff--- I understand the knee jerk reaction is to reinsert. But perhaps it is better to think about how to restate the two properties which no longer appear and are essential--- linearity and degeneracy--- in a less formal way, with examples.Likebox (talk) 20:43, 13 June 2008 (UTC)


 * Sorry, I think I sound like a jerk above--- a lot of the material from before was valuable, and I tried to reinsert it today. My main complaint with the old stuff was just that it was difficult to read because of too much detail, detail which I think must be left to the reader to puzzle out lest the article get bogged down with too many steps. Perhaps the current version is too terse, but I hope the flavor of the previous presentation is preserved. I apologize for any rudeness above--- I appreciate the effort that clear mathematical exposition takes.Likebox (talk) 07:28, 15 June 2008 (UTC)

The proof of nondegenerate ground state?

 * The timestamp "15:36, 9 September 2008 (UTC)" reflected the time of only the belated signing by the contributor of the original text, and has now been replaced by the times of the text contribution and of the author's retractions via strikethru.

The section "nondegenerate ground state" contains an incorrect proof that the ground state of a Schrodinger equation is a nonnegative function and nondegenerate. A while ago the proof was replaced by a better one but then reverted back.

I located this wikipedia article while looking for a proof of this well known property. While it is not clear whether the proof belongs here in this article, let me first say why the proof as it stands is wrong. The proof is based on the variational principle. The proof shown currently is that if $$\psi(x)$$ is a test function that changes sign and minimizes the energy functional $$\langle \psi | H | \psi \rangle$$ then we can take $$|\psi(x)|$$ as another test function that has the same integrals of potential and kinetic energy, except for the kink at the place where $$\psi(x)=0$$. The kink should then be smoothed out, and the result is that we now have a test function that has a smaller value of the energy functional. This contradiction proves the statement.

T his is incorrect because it's not true that we can always straighten the kink while not increasing the energy functional. An easy counterexample is $$\psi(x)=x$$ and $$V(x)=0$$. The kinetic energy of this $$\psi(x)$$ is identically zero, so $$\langle \psi | H | \psi \rangle=0$$. If we now take $$|\psi(x)|$$ and straighten the kink, the kinetic energy is going to be strictly positive no matter how smoothly we straighten it. So the new test function has always a strictly greater value of the energy functional. This counterexample shows that it is not possible to smooth the kink as required.

The proof that was deleted by an edit on 31 August was better: it allowed a small increase of the energy functional while straightening the kink.

I'd like some experts in mathematical physics to examine this argument. In my view the proof of this important statement needs to be either presented clearly and correctly, or removed and replaced by a reference to a textbook. Sznagy (talk) 14:35, 9 & 13:52, 11 September 2008


 * The proof is correct, but must be stated in terms of the integrated by parts version of the action. THe reason your counterexample doesn't work is because it doesn't satisfy the condition that integration by parts works--- it grows at infinity. The expression for the energy used in the variational principle integrates by parts to replace psi grad-squared psi (which gives zero for your example) with grad-psi-squared (which is infinity for your example). This replacement is only allowed if boundary terms vanish (the boundary terms are infinite for your example).


 * Using the grad-psi squared energy expression, rounding out any kink always reduces the energy. This proof is presented in many textbooks.Likebox (talk) 17:43, 9 September 2008 (UTC)


 * Thank you for clarification. I was thinking about a function $$\psi(x)=x$$ only near $$x=0$$ so that the boundary conditions are satisfied. Actually I think my mistake was very simple: I forgot the minus sign in front of the second derivative


 * $$H= - \psi \psi^{\prime\prime}$$


 * Taking first $$\psi(x)=|x|$$ and then smoothing the kink, we get a function whose second derivative is everywhere nonnegative. Then the minus sign makes a negative extra contribution in the kinetic energy. One needs to make sure that it's possible to make the kink smooth without adding too much to the potential energy, so that the total change in the energy is strictly negative, but I presume this can be verified with some epsilon-delta work.


 * The proof does not need to be changed at all.


 * Sznagy (talk) 20:12, 9 September 2008 (UTC)


 * On the other hand, there is the case of Fermions. For N-fermions I am not sure that the uniqueness proof works--- there is the additional restriction on phase space to remove multiple copies and the wavefunction vanishes on the edges. For Bosons, everything is fine. In principle I think it should work for Fermions too, but there's the sign problem, and I'm a little confused. In 1d, the proof can be extended to fermions by poor-man's bosonization--- just think of the fermions as infinitely repulsive bosons.Likebox (talk) 20:59, 9 September 2008 (UTC)


 * Actually I'm not sure that the statement is true for fermions. The fermionic wave function can be described as a solution of the Schr. equation that satisfies certain antisymmetry properties. So the ground state for fermions might be equal to an excited state that one would obtain by solving the Schr. equation without imposing antisymmetry. The excited state does not have to be nondegenerate. So it seems possible that the ground state for fermions might be degenerate. The same argument is perhaps not true for bosons, however. An explicit counterexample would help but my expertise is not sufficient to produce it right away. In any case we need to say that the statement is correct for 1-particle Schr. equation or for distinguishable particles. Sznagy (talk) 13:52, 11 September 2008 (UTC)


 * Stupid me--- of course you are right. You can take five noninteracting electrons and put them in a H atom, the first two in the 1S, the second two in the 2S, and the third in the 2p. That's a threefold degenerate ground state.Likebox (talk) 19:08, 11 September 2008 (UTC)


 * Thank you for the example. For bosons, the statement is true and the same proof can be used: if  $$\psi(\vec x_i)$$ satisfies the bosonic symmetry requirement then $$|\psi(x)|$$ also satisfies the same symmetry. So  $$\psi(x)$$ cannot change sign and cannot be degenerate. Sznagy (talk) 10:46, 12 September 2008 (UTC)

To hbar or not to hbar
The problem with all the hbars is that for a new person, each symbol is intimidating. The fewer symbols the better. In this case, the constant is only performing a unit conversion, and so should not be included except:
 * 1) When discussing historical work, when it sometimes makes the corresponding formula easier to find in the original
 * 2) When comparing to real systems with experimental data, when engineering units are conventional.

When talking about abstract theorems, like the positivity of the ground state wavefunction, the hbars only detract from the discussion. Simularly for unitarity, or any other mathematical property.Likebox (talk) 18:48, 1 October 2008 (UTC)


 * I agree with you, the fewer the symbols the better. Why don't we go a step further "To h or not to h"? Planck's constant h is also just a conversion unit and could be left out to the benefit of better insight. Then Schrödinger's equation appears to be valid also for ordinary macroscopic objects, see v:Image:QM_1st_law.gif. Arjen Dijksman (talk) 07:41, 4 October 2008 (UTC)


 * If hbar is one, then h is 2pi, and that is the difference between using radian measure for angles vs. a measure where the 360 degrees is "1" unit. I think the standard radian way is clearer, so h is just 2pi. It's dimensionless, but its not equal to 1. There is another place one should use hbar that I forgot about that you brought up:
 * 3. When discussing the classical limit, which is a scaling limit where hbar is small. In terms of dimensionless numbers its complicated to state, since many different quantities can be large to reach the classical limit.

Any usage of natural units is going to confuse the laity, so we should eschew them. I don't see that hbar is any more confusing than just h. --Michael C. Price talk 15:48, 4 October 2008 (UTC)


 * Hopefully when this project is done, there will no longer be a laity. Everyone will know everything.Likebox (talk) 02:26, 5 October 2008 (UTC)
 * That's a nice hope, but that doesn't mean you should start writing articles like everyone knows everything. Most introductory quantum mechanics textbooks I've seen don't use natural units, and many readers of this article won't even have read an introductory text.  You certainly can't expect them to be familiar with natural units.  Leaving them out makes the equation more confusing, and I'd argue is actually more intimidating.  Saying "h-bar is a constant equal to roughly 1.05×10^−34 J·s" is far less intimidating than saying "in this equation, length and time have the same units".  One requires familiarity with a new concept, the other just introduces a new number. -Tim314 (talk) 02:12, 29 November 2010 (UTC)

I strongly suggest that we include all hbar's (and no h's, for consistency). I agree each symbol is intimidating, but even worse is confusion. People introduced to the schrodinger equation will *not* intuitively understand that by setting hbar=1 you can measure momentum in units of distance. They will just see a massive discrepancy between their textbooks and this page, as well as not understand why the units don't seem to work. Furthermore, it appears someone set m=1 in the section on the green's function, which is an even bigger source of confusion. I do this crap for a living, and I was confused. Njerseyguy (talk) 06:08, 2 July 2009 (UTC)


 * Yes. Hbar all over! If you are used to the hbar-less notation, you can set them to 1 in your mind. However, if you aren't used to the hbar-less notation, you won't know where the hbars would be, were they not set to 1. Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 06:21, 2 July 2009 (UTC)


 * You can figure out where all the hbar's go by dimensional analysis. The reason to omit hbar is that it is, like the speed of light, a nuisance constant, which only distracts from the meaning of the equation. It should never appear except when doing history, comparing to experimental data, or taking the classical limit.Likebox (talk) 17:48, 26 February 2010 (UTC)


 * Hbar, please. Far easier (for myself and other dumbasses) to set hbar=1 than to figure out where it should be.  I looked through 3 different college physics books on my shelf and none of them use natural units.  I'm not saying natural units is "wrong", just makes a hard topic an even harder slog for the poor bastards like me trying to follow this stuff.  Pity me and laugh derisively if you must, but it honestly would make the article better for most people trying to learn this stuff.  CosineKitty (talk) 03:01, 27 February 2010 (UTC)


 * Livebox, your opinion that h-bar or c "should never appear except..." doesn't seem to be shared by any author of introductory physics texts that I've ever read.  I can't think of any undergraduate-level text that uses natural units exclusively.  (Feel free to contradict this with examples.)  And would you really want an article introducing the constant speed of light to say "the speed of light is constant, and is equal to 1"?  That statement would be incomprehensible to 99% of Wikipedia's readership.  Whereas, "light moves at 300 million meters per second" is comprehensible to a ten-year-old. -Tim314 (talk) 02:52, 29 November 2010 (UTC)

Lots of repetitions
Once were done with restoring the hbars, I suggest we tackle on the length and verbosity of this article. There's just too many repetition, the structure is too fine-grained, and many sections go on and on with little benefit to the article. Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 21:51, 27 February 2010 (UTC)


 * The article does not repeat itself anywhere, and you restored the hbars and c's incorrectly nearly everywhere!Likebox (talk) 22:43, 27 February 2010 (UTC)


 * Please, if you insist on restoring hbars, at least do so correctly. Also, the "repetitions" in this article are the variational principle, which is repeated for a reason--- the first time it is done in function space, the second in general vector spaces, and the second is more general. The other "repetition", Galilean invariance, is done in detail for one particle, then for many particles later on. Neither is repeating, since the second occurence expands and generalizes the first.Likebox (talk) 22:52, 27 February 2010 (UTC)


 * I will ask that this page be locked if you continue to do this--- this is pure vandalism--- I told you that the hbars are incorrect, please take the time to do correct edits.Likebox (talk) 23:03, 27 February 2010 (UTC)

Rewrite
Alright, since Likebox decided to take his ball and go home, I guess this means we have a mostly clean slate on what to write and how to structure the article. I propose a rough structure that would more or less follow this:


 * Lead + formal Schro eq.
 * History
 * Derivation
 * p and x operators


 * Properties of Schro eq
 * Time indep
 * Textbook applications (free particle, particle in a box, finite potential well, ...)
 * Time dep
 * Textbook applications (wave reflection against a wall, wavepacket spreading)


 * Refinements (Non-linear Schro eq, Dirac eq, etc...)
 * See also

It'll be easier to rewrite this article from scratch, than chase for sources we might not be able to find. Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 01:46, 1 March 2010 (UTC)
 * Support proposal as stated above. I agree with your proposed structure and having a clean slate, about what should be written. I say begin right away. It will be better anyway since I doubt very much you will try to supply fringe, non-mainstream, sources (if you get my meaning). I am willing to take an educated guess that consensus will back you on this. Go for it dude. Steve Quinn (formerly Ti-30X) (talk) 23:09, 1 March 2010 (UTC)
 * Quick comment: The introduction seems to be clearly written. However, I only have very basic, general understanding regarding SE, and its been awhile since I read anything about it. So, I couldn't say if the introduction is accurate. Only that it is clearly written. Steve Quinn (formerly Ti-30X) (talk) 23:21, 1 March 2010 (UTC)


 * Against. Cleaning the slate will lose information. --Michael C. Price talk 10:39, 2 March 2010 (UTC)
 * Good editing means knowing what to throw away out and knowing what to keep. We can always compare against the old version and see if there is something missing. If people think something is missing that should be added, then it'll be added back. Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 15:30, 2 March 2010 (UTC)


 * I do not see the need to start from scratch now you already made lots of decisions of what to not include. If there are unsourced sections with problems finding a source then delete, but otherwise I think we can work from what we have now. -- Bduke   (Discussion)  21:28, 2 March 2010 (UTC)
 * I guess I should have been a bit clearer. I meant rewriting "from scratch" as in not bothering to restore the stuff that was recently removed and find sources for it, but rather expand the article as needed to achieve whatever content we agree upon. Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 21:41, 2 March 2010 (UTC)

Hi, a new anon editor with an interest in this article noticed my name in the history from a vandal revert and left a message for me regarding this article. Since I only have a basic understanding of quantum physics, I'm really not the best person to deal with it, so I've copied the message here. Wine Guy ~Talk  00:10, 17 March 2010 (UTC)

Copied from User talk:Wine Guy I have seen that a couple of people have suggested an addition to the article that would show the separation of the time-dependent wave function into a product of a time function with a space function, leading to the time-independent form of the Shroedinger equation. This addition would only take a couple of lines, and in my opinion considerably reduce the voodoo factor. Anyone who knows how to take a derivative would follow the logic, even if they had never seen the Schroedinger equation. I hope you will add the needed lines to the article. In the meantime, I will try to learn how to make the changes myself and post it to see if it will be accepted. 76.248.144.40 (talk) 21:43, 16 March 2010 (UTC)

Wrong powers of hbar make a joke out of this article
I am personally embarassed to have an equation that reads:


 * $$ \hat{H} = -{\hbar\over 2m} \nabla^2 + V(x)$$

This is not bad mathematical writing anymore--- it is pure illiteracy.Likebox (talk) 23:08, 27 February 2010 (UTC)
 * WP:SOFIXIT -- Bduke   (Discussion)  23:25, 27 February 2010 (UTC)


 * It wasn't broken to begin with!Likebox (talk) 23:26, 27 February 2010 (UTC)


 * Ok, now at least the powers are correct in the places I've checked.Likebox (talk)


 * I don't think headbomb did anything other than replace "k" with "hbar k", "laplacian" with "hbar^2 laplacian", and "d/dt" with "hbar d/dt". This is appaling. He didn't check the units on the equations, some of which are still in natural units, even in sections he covered. I am not goint to assist in butchering my own mathematical prose, of course.Likebox (talk) 09:32, 28 February 2010 (UTC)

This article is mostly unsourced
Where are the sources?Likebox (talk) 16:36, 28 February 2010 (UTC)
 * Well, you are writing the article, so you should know. The job of a wikipedia editor is to write from sources, to summarize what others have written. You are not supposed to write out of your head and then look for sources. -- Bduke   (Discussion)  20:43, 28 February 2010 (UTC)


 * You're absolutely right.Likebox (talk) 22:31, 28 February 2010 (UTC)


 * I cleaned it up now. I'll try to do the same for similar articles I contributed to.Likebox (talk) 22:40, 28 February 2010 (UTC)

Numerical Solution of Schrodinger Equation
This online software Periodic Potential Lab solves the time independent Schrodinger equation for arbitrary periodic potentials which might be impossible analytically. Does it seem good ides to link it here? (talk)

Missing hbar's in Version-> time dependent equation.
It appears to me that all the hbar's are missing in this section, after the following text:

"For the specific case of a single particle in one dimension "

Can somebody confirm please.

Peeter.joot (talk) 15:39, 1 December 2008 (UTC)


 * See the discussion above, I believe they are using natural units. 24.201.18.145 (talk) 20:28, 14 December 2008 (UTC)

I've added them. Is there a wiki-standard about the use of natural units? --Michael C. Price talk 11:19, 2 July 2009 (UTC)

Density functional theory
The following comment was posted in the Article itself by unidentified user instead of here: "* Density functional theory (need verification, as far as I know, DFT will give you the PDF, from which it is impossible to deduce the wavefunction)" Yours sincerely, GeorgeLouis (talk) 05:12, 11 July 2009 (UTC)


 * It is possible to deduce everything from the ground state PDF in the case of a Hamiltonian of the form T+V (of Schrodinger type), which was Kohn's theorem regarding this. The proof is trivial--- the ground state PDF uniquely determines V, which uniquely determines the wavefunction of all excited states.Likebox (talk) 17:37, 26 February 2010 (UTC)


 * Sorry, I remembered the correct Kohn proof, not the triviality I wrote above. The same holds for electrons with mutual electrostatic repulsion in an external potential--- the ground state electron density (not even the wavefunction, just the total electron density, a function on space) determines the potential, and therefore all the energy levels.Likebox (talk) 13:45, 27 February 2010 (UTC)

What Are you Tagging regarding "Short heuristic derivation"?
What part of the derivation do you find controversial--- this is a mathematical text, so unless you discuss, it is impossible to know what you want.Likebox (talk) 17:08, 26 February 2010 (UTC)
 * I'd like to see a reference to a textbook doing a similar derivation. This not just a matter of WP:V, but also a matter of providing the reader with good entry points into the literature. TimothyRias (talk) 17:30, 27 February 2010 (UTC)


 * No problem, will do.Likebox (talk) 20:47, 27 February 2010 (UTC)

No to natural units
Any person can set hbar = 1 and retrieve


 * $$i \frac{\partial}{\partial t}\Psi(x,\,t)=-\frac{1}{2m}\nabla^2\Psi(x,\,t) + V(x)\Psi(x,\,t).$$

Very few can place the hbar in the correct places of above and retrieve the correct hbarred version


 * $$i\hbar\frac{\partial}{\partial t} \Psi(x,\,t) = -\frac{\hbar^2}{2m}\nabla^2\Psi(x,\,t) +

V(\mathbf{r})\Psi(x,\,t)$$

Purge natural units completely from this article, except when natural units are specifically discussed (which really should not be more than mentioning that setting hbar = 1 gives the natural units version). Using natural units completely obfuscates the derivations, and introduces an unnecessary barrier to comprehension. Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 19:42, 26 February 2010 (UTC)


 * Which is more trivial, restoring hbar by dimensional analysis, or removing by setting = 1? The latter, of course, so remove natural units. --Michael C. Price talk 10:33, 1 March 2010 (UTC)
 * This is completely wrong, as was discussed above. The hbars are trivial to restore by dimensional analysis, and their presence in mathematical sections just causes unnecessary trepidation among students. When doing the mathematics of quantum mechanics it is as important to set $$\hbar=1$$ as it is to set c=1 when doing relativity.


 * The only time hbar should appear is:
 * When discussing historical material
 * When comparing to experimental data in engineering units
 * When taking the classical limit


 * Other times, it is not only inessential, it is uglifying and prevents easy entry of equation into head. It makes obvious things look nonobvious.Likebox (talk) 20:09, 26 February 2010 (UTC)

It's completely unreasonable to expect the average reader to perform this before being able to understand the article. WP:MOSNUM is very clear on this, and for a very good reason, we should write accessibly, for the widest audience possible:"Use familiar units rather than obscure units—do not write over the heads of the readership (e.g., a general-interest topic such as black holes would be best served by having mass expressed in solar masses, but it might be appropriate to use Planck units in an article on the mathematics of black hole evaporation)."

The reader is much more poorly served by natural units then without them, and the natural units version of the Schrodinger equation is also far less common. It's trivial to set hbar = 1. It's not trivial to see where the hbars original were. No reader is better served by setting hbar = 1, even if your field of expertise is QM. Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 20:31, 26 February 2010 (UTC)


 * I am telling you, not as any sort of expert contributor but from my memories of struggling to learn this many years ago, that the hbars are obfuscatory and do not add to understanding. I have no doubts about this. When I first learned the Schrodinger equation it looked like this:


 * $$ E\psi = {h^2\over 8\pi^2 m} {\partial^2 \over \partial x^2} \psi + V \psi $$


 * How was I supposed to know that the numerical factors are inessential gibberish? The only way to present this correctly is to go to natural units, and to say clearly that wavenumber is momentum, and frequency is energy. This is exactly analogous to relativity.


 * I am 100% sure that it is more accessible to people in natural units rather than less.Likebox (talk) 20:58, 26 February 2010 (UTC)


 * I first learned the Schrodinger equation when I figured out that you can set hbar to 1, and then the above becomes


 * $$ E \psi = ({\partial^2\over 2m} + V) \psi $$


 * So that it is obviously the same as kinetic plus potential energy, with Schrodinger's derivative substitutions. The factor of "2m" on the bottom is essential for readers to recognize "p^2/2m"--- it is required psychologically for new learners.


 * The other thing is, if you don't set hbar to 1, you make a false distinction between energy and frequency, so all the exponential factors are either written in terms of frequency differences, or have ugly hbar factors in them. It is impossible to keep the math straight in your head without natural units, nobody who can actually calculate anything uses hbars.Likebox (talk) 21:08, 26 February 2010 (UTC)


 * And I'm 1000% sure that it isn't. The ħ is way too important to ignore, it comes into play into all sorts of relations (especially when the commutator is concerned), hilbert spaces, operators, etc... If you want natural units, set hbar to 1 in your own mind. It requires a lot more effort to do the opposite. In the exact same way that we say the Planck relation is E = ħ&omega; (or E = h&nu; if you are the unbarred kind of person), and not E = &omega;. It would make as much sense to present the heisenberg uncertainty relationship as &Delta;x&Delta;p ≥ 1/2. Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 21:09, 26 February 2010 (UTC)


 * And keep you're personal attacks such as "nobody who can actually calculate anything uses hbars" to yourself. I use 'em, and I sure as hell know how to fucking calculate my way around the Schrodinger equation and beyond. Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 21:13, 26 February 2010 (UTC)

(deindent) I wasn't making personal attacks--- I didn't even know you use hbars in life! I thought you just wanted them for the article. Really, nobody who can calculate anything uses hbars, no offense intended.

Again, nearly all theorists beyond the undergraduate level say exactly "E=&omega;". Experimentalists only don't do that because they need to use engineering units for their devices. Also, nearly all theorists say Δ x Δ p > 1/2. There is no reason to tote around hbars, or to make false distinctions between energy and frequency, between momentum and wavenumber, or between angular momentum and an integer.

The hbar does not come "into play" anywhere--- it is just "1", exactly like the speed of light in relativity. The commutation relations do not need hbar, they are just [x,p]=i. The "hilbert space operators" are trivialities, and every theorist in the world uses natural units.

Irony of ironies: I am surprised that on this page you are arguing Brews ohare's position regarding a fundamental constant.Likebox (talk) 21:17, 26 February 2010 (UTC)


 * Again, no they don't. I can quote you several publications dealing with the intricacies of the Schrodinger equation, all which used hbars, and which are well-beyond the undergrad level. And even if they did not use hbars, it's no reason for us to be writing above the level of undergrads, whose textbooks all include the hbars. And no I'm not arguing Brews' position on this, because no one of us talked of setting c = 1 in the speed of light article, and Brews never had to "oppose" the setting of c = 1 in the article. Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 21:23, 26 February 2010 (UTC)


 * This is exactly Brews position. He was opposing the setting of "c=299whatever m/s", which is exactly the same as setting "c=1", except less convenient. You are opposing setting hbar to 1, and arguing that hbar has real meaning. Different constant, same position.


 * Most historical sources (from before 1960) use hbars pretty often, although in private calculations I have never seen anybody use them. Sources from recent years do not use hbars, especially at a more advanced level. This article mixes the two, to get readers accustomed to both conventions. I only got rid of the hbar when it obfuscates the mathematical reasoning with trivialities.Likebox (talk) 21:31, 26 February 2010 (UTC)

You two are making the Physics Project a bearpit. I use natural units all the time, but as a computational quantum chemistry, I call them atomic units. However, they should not be used in wikipedia unless we are specifically talking about them. Equations in wikipedia should be such that the student can do a dimension analysis using SI units as a guide. To miss out h-bar is much more confusing. Energy is NOT frequency. So I agree with Headbomb, but he should stop swearing here. -- Bduke   (Discussion)  21:40, 26 February 2010 (UTC)


 * I think you are under the impression that it will be pain-free to impose this convention. It will not--- Energy and frequency need to be identified for all quantum field theory pages, to prevent monstrous prefactors of hbar and c, and for string theory, it is important to go further and set some form of the gravitational constant to 1. I think that mixing conventions is not a problem, so long as you say "in natural units" somewhere clear.Likebox (talk) 21:45, 26 February 2010 (UTC)


 * Is it just me, or are Bduke and Headbomb disrupting this page?Likebox (talk) 21:47, 26 February 2010 (UTC)


 * Ignore above "joke", and return to the topic. I am prepared to accept that some very advanced articles might, at some point after clearly indicating the change, move to use natural units, but this should not apply to articles like this one, which fairly junior students might access and not just physics students, but chemistry and other students. It should also not apply to the start of advanced articles, which should simply explain what the topic is about. Likebox, I suggest our differences are because you, above, describe this as a mathematics article. I take real issue with that. It is a physics article. Physics is science; mathematics is not. Here, mathematics is just a tool. Avoiding natural units is more closely following the science, certainly for people just setting out to understand quantum theory. I totally oppose the use of natural units in this article and indeed more widely on wikipedia. -- Bduke   (Discussion)  00:00, 27 February 2010 (UTC)

(deindent) The disruption comment was meant to point out the parallels with User:Brews ohare's position on units in Speed of light, and the endless accusations of "disruption" for editors that bring up the issue of fixing the speed of light to be a constant. Fixing hbar to be a constant is no different.

But your proposal is incredibly ridiculous. It will stunt the ability to write every article on quantum mechanics: am I supposed to write


 * $$ e^{i{(E_i-E_j)t \over \hbar}}$$

as opposed to the natural


 * $$ e^{i(E_i - E_j)t}$$

for every single phase factor in a matrix element or in perturbation theory? Are we supposed to duplicate all symbols, using both "p" and "k" for momentum and wavenumber separately? And "w" and "E" for frequency/energy?

Are we supposed to write:


 * $$ \int d^4k\over \hbar^4 $$

For Feynman diagram integrals? Not only is that silly, it is against all conventions.

To avoid natural units is a waste of letters, and adds a layer of confusion to already confusing topics.

I have a better suggestion, whoever writes the exposition chooses the units. If you've not written any mathematical exposition of quantum mechanics, you have no idea how annoying it is to use engineering units.Likebox (talk) 00:15, 27 February 2010 (UTC)

This is not a better suggestion. It would merely add confusion. The discussion on this topic is spread between this section and another section further up. Overall, I can see no support for you and several editors supporting the retention of hbar. The consensus is not running your way. I did suggest a compromise, that hbar would be used in all articles likely to attract a readership from undergraduate beginners and allow more complex and advanced articles to change to natural units in advance sections after the introduction. BTW, they are not engineering units; they are science units. It does not help your case to describe the arguments you oppose as "incredibly ridiculous" and "silly". Please assume good faith. My argument regarding beginning approaching the topic is supported recently by another editor in the section further up, and by Headbomb and Michael Price. -- Bduke   (Discussion)  04:02, 27 February 2010 (UTC)


 * I was able to convince those other editors with a quick comment--- the fact that newcomers don't see the benefit of natural units is not "consensus", it just means that there are a lot of people in the world who have never written about quantum mechanics and thing "what's the harm of a few hbars"?


 * I support your compromise, if you add the word "partially", because those young people should be gradually getting used to an hbar-free environment. I didn't get rid of all the hbars here, just the sections where it should be confusing.


 * Your arguments are given in good faith, but from lack of experience. This is also true of the many other people who commented above. It is important that you try to write some quantum mechanics before you make suggestions for what units to use.


 * Headbomb and Michael Price aren't arguing for this anymore. I think It's just you and me. Don't look at dead discussions, because they are irrelevant. People can be persuaded you know.Likebox (talk) 04:08, 27 February 2010 (UTC)


 * You cannot seriously interpret a not even 8-hour silence from someone as meaning that they aren't "arguing for this anymore", and what in the world does Michael C Price has to do with anything? The guy hasn't edited this page since summer 2009. Advanced QFT is not basic QM, and I've yet to see who you've convinced with your "quick comment". You don't have consensus for using natural units, so i suggest you drop the issue and move on. Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 05:01, 27 February 2010 (UTC)


 * You don't have consensus for unnatural units either. If you haven't written mathematical expositon of quantum stuff, I think that you don't know how absurd toting hbars around becomes. They always occur in the combination "hbar derivative" "Energy/hbar" "hbar omega" "hbar k", it's like a stutter. You know when they're coming, its determined by dimensional analysis, and they are like as annoying as a skipping record.Likebox (talk) 07:18, 27 February 2010 (UTC)

(edit conflict) Likebox, how do you know what my experience is? I have been teaching students about the Schrödinger equation for close on 50 years. OK, these have been physical chemistry students, but they are going to come to this article too. It is not just for advanced physics students. It might even be read by someone who left school at 14, but has heard of Schrödinger's cat and wants more information about what Schrödinger did. Look at the contribution above from CosineKitty. That supports my view. My compromise was only about more advanced articles than this one. I do not support using natural units on this article. Headbomb is correct. You do not have consensus for using natural units. You do not seem to understand the use of consensus. You have tried to convince people, as you should to get consensus, but I do not see that you have convinced anyone. Make sure the basic QM articles are free of natural units and then move on. -- Bduke   (Discussion)  07:25, 27 February 2010 (UTC)
 * Re above. You certainly do not have consensus. You are one against several. -- Bduke   (Discussion)  07:25, 27 February 2010 (UTC)


 * I used natural units for the whole article, but hbars were restored. I removed them only in some sections, where they are obfuscatory. I insist that the factors of hbar and c not be used for anything involving the Klein Gordon operator, which is incomprehensible in unnatural units.


 * You don't have consensus either--- You just showed up, and others were persuaded not to muck around with the units after trying to put all the hbars in, and seeing how much of a mess it made.


 * I expect all people, including lay-people, to be able to understand how to convert units, and how to reinsert hbars or remove them. The mix of hbar and no hbar is ok as it is.


 * I also strongly recommend to you that you start to use natural units in your teaching as well. It will make perturbation theory much easier.Likebox (talk) 07:39, 27 February 2010 (UTC)

I am now going to leave it for others to comment. Let us however be quite clear. First, you can not insist on anything here. If you do you are likely to be blocked. Second, you have not persuaded anyone. Third, I may not have edited this article recently, but I can still comment. Indeed I have as much right to do so as you have. In fact I suspect I have been watching this since long before you started on wikipedia. Finally, I am well aware of the use of atomic units. I use them in my research and with postgraduates. I did not use them with second year chemists. Have you any experience with teaching beginners QM from a non-physics background? -- Bduke   (Discussion)  08:08, 27 February 2010 (UTC)


 * I can insist all I want. Insisting is not grounds for a block. I will also keep arguing, because I have a little more to say. You can say whatever you want, I can say whatever I want. Of course I have taught undergraduates quantum mechanics, and I find that a simple discussion of units, setting hbar=1, setting c=1, at the very beginning, is the most effective way to get them to focus on the content of the material and not the form. This makes DeBroglie relations into identities, etc.


 * However CosineKitty's comments are starting to get to me: is it really that difficult to follow natural units, when they are announced so prominently at the beginning of each section, and linked? Is it really that hard to understand that if "Et" is treated as dimensionless than hbar has been set to one, or else there is an implict hbar dividing the exponent? Is it really best to hide from students the way that all professionals actually work with the equations, and make them tote hbars around? It's not a trivial thing--- every time you take a derivative you have to write one more symbol, your efficiency in calculating is destroyed.Likebox (talk) 12:27, 27 February 2010 (UTC)
 * Well I will come back on this. I am glad that CosineKitty's comments are starting to get to you. Yes, it it is that difficult. Saying that energy = frequency is very confusing. Putting a quantity with units to unity leads to confusion. It asks you to say that apples = oranges. -- Bduke   (Discussion)  12:47, 27 February 2010 (UTC)

(deindent) You see, with this statment, you are simply wrong. You are making the exact same statement that Brews ohare was making regarding the speed of light, that units of time are essentially different from units of space. I have long ago stopped seeing hbar (or c) as a quantity with units, and just like c=1, I think in hbar=1. So that to me, energy and frequency are synonyms, as are momentum and wavenumber (in appropriate context). The idea that the number and type of units we should use is given by god is silly. There are no units--- Quantum Gravity is ultimately dimensionless.13:01, 27 February 2010 (UTC)


 * I agree here, but we have to deal with generations of people who are indoctrinated with the idea that dimensions/untis do have fundamental meaning. Just read this article and in particualar the included Referee reports. It is like questioning the existence of God in the year 1700. Even when talking to rational scientists, you would not make much progress. Count Iblis (talk) 13:12, 27 February 2010 (UTC)


 * It's interesting that you would make the parallel to the existence of God. I think that it's only the existence of a demiurge that was contested by science. God is a subtle concept, and not all interpretations are excluded by science. In particular, some interprertations of God don't involve a "creator of the universe" or any supernatural phenomenon, and basically amount to no more than the prediction "things will work out with time, even though all human beings are corrupt". In particular, the modern faith of some people (especially American politicians) is of this non-supernatural sort.Likebox (talk) 13:22, 27 February 2010 (UTC)


 * Let's leave theology out. It doesn't matter what you personally prefer, the point is that everything in the undergrad level, and very often in the post-grad level is done with hbar-s and c-s. No one used to setting hbar-s and c-s is unable to set hbar and c to one in his own head, however no one unfamiliar with natural units will be able to place the hbar-s and the c-s at the correct places, if they want them, without spending several hours looking up how in the world you retrieve them, or doing the math from the start, with hbar-s and c-s.


 * Even though most particle physicists are perfectly comfortable saying that a proton of mass 938 MeV, moving with a momentum of 30 MeV, on Wikipedia we usually say 938 MeV/c2, moving with a momentum of 30 MeV/c. Why? Because otherwise we lose most readers, who'll "What do you mean a momentum equal to MeV's? MeV's are units of energy!".


 * Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 14:12, 27 February 2010 (UTC)


 * So far, the argument for using natural units in this article seems to favor some advanced practitioners' needs (so far, Likebox only), while everyone else is pointing out that the less experienced (like me) will be hindered. I don't think anyone has provided an explanation of how using hbar will confuse the more experienced; only that it annoys some of them because it makes the equations bigger and maybe less elegant-looking. (Likebox, I'm trying to paraphrase an opposing point of view, so please be gentle in correcting me if I'm putting the wrong words in your mouth.  I'm not intentionally presenting a straw man argument, even if it looks that way.) But I make the same argument here that I would if someone suggested we write E=m in mass–energy equivalence instead of E=mc2: why favor the advanced reader (or the article's advanced writer) over the student, in an introductory article about the topic?  And I certainly would not mix natural and conventional units in the same article: that would be an even worse confusion.  CosineKitty (talk) 16:59, 27 February 2010 (UTC)

(deindent) CosineKitty--- I respect your position--- but I would like to have your opinion after you read the article in depth, and try to understand everything. Superficially it seems that the hbars will help, but I assure you that the opposite is true.

It is not just annoying to do this, it is a matter of bad mathematical writing. I tell you, this is not as an experienced editor, ever since I was 16 years old, if I saw something that wasn't in natural units (like proton mass in MeV/c^2 instead of in MeV) it flashed in bright lights "this was written by an incompetent-- DO NOT READ THIS TEXT". It's a warning sign for a bad physicist, like "It was a dark and stormy night..." and "Bang! Bang! Went the gun!" is a sign of bad writing. I don't want stuff that I wrote to read this way.Likebox (talk) 20:53, 27 February 2010 (UTC)


 * Also for CosineKitty: This is extremely important--- hbars and c deface the fundamental meaning of equations, and make it impossible to understand the equations in depth, because they are littered with crap. For complex equations, like Hawking radiation formula, most of the symbols in the equation are just litter.


 * The black hole temperature in natural units is


 * $$ T={1\over 8\pi M} $$


 * It says: the black hole gets bigger and more massive, it gets colder, and it's temperature is one planck unit when its mass is 1/8pi. The radius of a black hole in natural units is twice its mass. A glance at the equation reveals the meaning. Do you recognize the following here:


 * $$T={\hbar\,c^3\over8\pi G M k_b}\,$$


 * This says the same exact thing, except littered with crap, so that all the interesting parts are drowned out in crap constants that don't reveal anything except how we humans made bad unit choices in the past. You can reconstruct all the G,c,hbar, and k_b's from dimensional analysis uniquely, if you even have to, which is never. Just remember what a Planck length, a Planck time, and a Planck energy is.


 * For specific examples relevant: lets start with the energy momentum relation in relavity:


 * $$ E^2 - p^2 c^2 = m^2 c^4 $$


 * Now let's do a substitution for Schrodinger operators to get the Klein Gordon equation:


 * $$ \frac {1}{c^2} \frac{\partial^2}{\partial t^2} \psi - \nabla^2 \psi + \frac {m^2 c^2}{\hbar^2} \psi = 0. $$


 * Again, everything is litter. I don't think you appreciate how distracting this type of litter is to students. This screams "whoever wrote this is an incompetent physicist", and if I saw this at age 16, I would not read the article.


 * The correct expressions are:


 * $$ E^2 - p^2 = m^2 $$


 * Which reveals itself to say that the four-dimensional length of the energy-momentum four-vector is the mass. THe Klein Gordon equation is:


 * $$ (\partial_t^2 - \partial_x^2 - \partial_y^2 -\partial_z^2) \psi= - m^2 \psi $$


 * It's the same thing, except replacing energy/momentum by derivatives. The issue is important--- students will not recognize the identity of the form when it is littered with irrelevant constants. Experts have to sit down and rewrite the thing without the constants to understand what it is saying. Nobody is well served by having the constants there.Likebox (talk) 21:16, 27 February 2010 (UTC)
 * Actually the expamples you give are very good examples of why it is useful to write factors of hbar,c and G. Writing them in the Hawking temperature for example immediately tells any competent physicist that this is a quantum gravitational effect. A fact that is not apparent in the expression in natural units. hbar,c and G provide the scale of different expressions immediately telling you which terms are and which terms are not relevant at a certain scale. As another example writing the factors of c in the Klein-Gordon equation is extremely useful if you want to see that the Schreodinger equation is the non-relativistic limit of this equation.
 * Likebox please also rememb er that theoretical physics =!= HEP. Whereas high energy physicist generally natural units (because they are generally looking at situations where velocities are of order c and actions of order hbar), this is generally not the case in other areas of theoretical physics. I regular here the low energy staff members at our institute scuff at the inability of students to gauge the magnitude of a result because they are so used to express things in natural units. TimothyRias (talk) 12:29, 28 February 2010 (UTC)


 * Oh no! Why aren't these students here? This is something they all understand, but nobody here does.


 * For taking the nonrelativistic limit, keeping c is useful. That and for historical material, and for comparing to experimental data. Everywhere else, it is a mark of bad mathematical writing. It is useless for checking material, and it is not required for order of magnitude.Likebox (talk) 16:09, 28 February 2010 (UTC)


 * To Headbomb--- restoring hbars and c's is a simple matter of dimensional analysis. Dimensional analysis is taught in high-schools. I don't understand where the block is to restoring them, if you even have to (which is never).Likebox (talk) 21:39, 27 February 2010 (UTC)
 * You have not addressed Headbomb's point seriously. If you get your way, and you are still a minority here, and use natural units throughout, you are basically telling chemistry students, engineering students and even first and second year physics students to not read this article. They have enough trouble checking dimensions in equations when they can support what they are doing with SI units. They would just be lost if you had your way. We are not really arguing about units. We are arguing about whether this is a mathematical article or a physics article, that people from other disciplines need to read; and about the whole level of the article and the target audience. You are making it too advanced for an encyclopedia. -- Bduke   (Discussion)  22:04, 27 February 2010 (UTC)

Another problem with natural units, that has so far not been mentioned, is that there are several different kinds of natural units. For example, Likebox writes:



E \psi = -\frac{1}{2m}{\partial^2 \psi \over \partial x^2} + V(x)\psi \,$$

while I and every other quantum chemist would write:

E \psi = -\frac{1}{2}{\partial^2 \psi \over \partial x^2} + V(x)\psi \,$$

using atomic units which gives the energy in Hartrees. This is adding confusion to confusion. The only way is to not use any variety of natural units. -- Bduke   (Discussion)  23:46, 27 February 2010 (UTC)


 * Atomic units are mostly a 1950's thing, and are of historical interest only. It is possible to use mass units so that the mass of the electron is 1, but then if you set c=1 your unit of energy is 511 KeV. These units discussions are ridiculous--- the page (and any other on quantum mechanics) is made much clearer by setting hbar to 1 for all intermediate steps, regardless of what you do with the mass of the electron and c.Likebox (talk) 23:57, 27 February 2010 (UTC)
 * Atomic units are very NOT of historical interest only. Many chemists these days use non-relativistic QM to calculate properties of molecules. They use atomic units and think of the Schrödinger equation as the second equation I gave above. Every graduate text on quantum chemistry or computational chemistry defines and uses atomic units. Your view of the readership of this article is far to narrow and you are ignorant of many fields of study that have an interest in this article. -- Bduke   (Discussion)  00:18, 28 February 2010 (UTC)


 * Atomic units are natural units with the further constraint that the mass of the electron is set equal to 1. Setting hbar to 1 is the minimal first step to natural units--- you can go further, or not. There is no reason to set the mass to 1 in a general article, where there can be several different types of particles with different masses, not just electrons as there is in quantum chemistry.Likebox (talk) 16:16, 28 February 2010 (UTC)


 * Natural units c=1, atomic units c=1/alpha. So if any c's are involved, it's hard to go from natural units to atomic units. Of course setting hbar to 1 will be correct for both, as you say. --Steve (talk) 23:29, 28 February 2010 (UTC)


 * I know that, and everyone else does too, and nobody uses atomic units anymore. m_e=1, hbar=1, and the bohr radius is your unit of length. But all you need to simplify calculations is hbar=1.Likebox (talk) 23:38, 28 February 2010 (UTC)


 * I think you're incorrect when you say "nobody uses atomic units anymore". I've taken two graduate-level physics classes in the past few years that were taught in atomic units. One was taught by a middle-aged tenured experimental AMO physics professor at Harvard, the other was taught by a middle-aged tenured theoretical mathematical-physics professor at UC Berkeley. I infer that atomic units remain reasonably common in some areas of physics. :-) --Steve (talk) 00:11, 1 March 2010 (UTC)


 * I pointed out above that "nobody uses atomic units anymore" is simply false, but Likebox ignores everything others say. Atomic units are universal in quantum chemistry, which probably involves more computer time solving the Schrödinger equation than any other area. However let me clarify that I am not saying that atomic units should be used. I am saying that hbar should be used, and one reason for this is that using one form of natural orbitals is confusing to people familiar only with another form. -- Bduke   (Discussion)  02:27, 1 March 2010 (UTC)

Implementation
Alright, I went through the article and restored the hbars and the cs. I missed some, one in Schrödinger equation, one in Schrödinger equation, and one or more in Schrödinger equation because I am unsure of how to unnaturalize them. Please double check my work to make sure I haven't forgotten some in other sections, or made mistakes on the way. Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 22:20, 27 February 2010 (UTC)


 * There is no consensus, nor implementation, and you have restored the hbars and c's incompetently. The energy momentum relation in relativity needs to match units, the Schrodinger operators were everywhere incorrect dimensions, and your edits were simply vandalistic. Please take the time and effort to check your own insertions before editing mathematical text.Likebox (talk) 22:54, 27 February 2010 (UTC)


 * I forgot to square, sue me. Instead of complaining about it, achieving nothing, why don't you correct these mistakes as you see them? Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 23:08, 27 February 2010 (UTC)


 * You didn't "forget to square". You inserted wrong powers of hbar everywhere, including in places where you don't need to square. Please stop editing this article incompetently--- you are doing harm to the text.Likebox (talk) 23:10, 27 February 2010 (UTC)


 * Yes, I DID forget to square, and that's pretty much all it was. Anything else, or are you gonna keep on ranting about my competence rather than focus on improving the article? Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 23:14, 27 February 2010 (UTC)


 * Again, no it WASN'T. You made mistakes in every single equation you modified except for one. The mistakes are still there, to my embarassment.Likebox (talk) 23:58, 27 February 2010 (UTC)


 * And yet you'd rather be vague and say "there are mistakes" rather than "when not in natural units, this equation should read as ... rather than as ... ". So either be part of the solution, or go away and let others do what you will not. Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 00:02, 28 February 2010 (UTC)


 * No. After seeing what you did, I'm just TESTING YOU to see if you can do it. This is a minimal competence requirement for editing a mathematical article on physics. I don't want to tell you the answer, and for most of the article, you won't find the answer in any book.Likebox (talk) 16:20, 28 February 2010 (UTC)

So you are not interested in improving the article? Then what are you doing here on the article's talk page?-- JohnBlackburne words<sub style="margin-left:-2.0ex;">deeds 16:24, 28 February 2010 (UTC)


 * THE RIGHT QUESTION IS "WHAT THE FUCK AM I DOING ON WIKIPEDIA"?Likebox (talk) 16:31, 28 February 2010 (UTC)

Likebox, ou keep claiming there is no consensus, when there clearly is as much consensus as one can normally get on an article like this. Your job, as Headbomb says, is to fix the errors, not remove hbar almost everywhere. Those removals were unacceptable. It has been discussed and several editors disagree with you. You are not God. -- Bduke   (Discussion)  23:19, 27 February 2010 (UTC)


 * As far as I can see Count Iblis and me support natural units, you and headbomb oppose, and CosineKitty is studying the issue to make an informed decision as a non-expert editor. I agree that it should be a mix of natural and unnatural units, but for some places, such as the Klein Gordon equation, there is no dispute in the real literature. Everyone writes it in natural units, and this is for a reason.


 * The current wording is absolutely unacceptable, since all the powers of hbar are everywhere wrong. This is not conventions anymore, it is illiteracy.Likebox (talk) 23:29, 27 February 2010 (UTC)


 * If you want to do a headcount, one the side of full hbars there is Headbomb (me), Bduke, Michael C Price, Njerseyguy, and CosineKitty. On the side of no hbars, there is you. Count Iblis, while sympathising with you on the issue of natural unit, also said we had to consider those who weren't familiar with natural units. So I'd be much more inclined to say that he's siding with us than with you. So if there's something wrong with the powers of hbars, fix it instead of ranting against them.Headbomb {{{sup|ταλκ}}<sub style="margin-left:-4.0ex;">κοντριβς – WP Physics} 23:34, 27 February 2010 (UTC)


 * NJerseyguy was persuaded that natural units are OK, and left years ago. Michael Price is still here--- why don't you ask his opinion? As for CosineKitty--- he is still making up his mind about this, so you should wait until there is consensus.


 * The issue here is that this is not obvious--- it takes thinking and writing before you appreciate the need for natural units. This article was written with natural units from the beginning, so you get scattered comments saying "why the natural units?" every few years. A simple explanation usually suffices.


 * Considering those that aren't familiar with natural units means putting a link next to every equation in natural units, and only using them in intermediate steps of mathematical derivations, not in the final formulas. This is what I did in almost all cases.Likebox (talk) 23:39, 27 February 2010 (UTC)

Having read the whole conversation and article, I feel strongly that we should use hbars everywhere. But the current situation where likebox uses them only in intermediate steps, with links, isn't terrible, and certainly isn't high on the list of the many problems affecting the quality of the article. I would still prefer to change them, but I don't care much.

I am a physicist, I know QFT, I know natural units inside and out. I do hope that everyone who cares about physics will eventually understand the Schrodinger equation and natural units. But we can't teach them both within the same article! Likebox, you seem to have the order backwards: You imply that people should understand how natural units work and then can learn and really understand the Schrodinger equation. That's not how it works in any physics course or textbook I've ever seen or been in or taught. Instead, people learn a bit of quantum mechanics, eventually understand what hbar is and what is the deep connection between energy and frequency, and only then start using natural units. --Steve (talk) 01:02, 28 February 2010 (UTC)

moved to Physics page...Chaosdruid (talk)


 * What a wonderful discussion, in which both sides are correct. If physics reveals that A is B, does that mean that all instances of B should be replaced by A? There is no general answer. It is simply a tautology. Energy is the capacity to do work. Frequency is oscillation. They are not the same in their definitions. But QM shows that frequency is a measure of energy (higher frequencies of light have more energy). Therefore, energy and frequency can be substituted for each other in any QM context. The equivalence principle states that gravity and physical acceleration are the same. I see this as similar in implications for natural units. I agree that we have made poor choices for standard units (Fahrenheit degrees), but I'm not sure that there can exist a single set of consistent constants and units that work in all physical contexts and regimes. David Spector (talk) 21:59, 26 November 2011 (UTC)