Talk:Planck constant/Archive 2

Citation Needed
This line seems to be unsubstantiated, although quite interesting: "Many scientists hope this does not mean the Planck constant is increasing as the Universe expands." --155.246.216.18 (talk) 03:23, 12 February 2008 (UTC)

The citation for the quote is Thematic Origins of Scientic Thought: Kepler to Einstein, revised edition by Gerald Horton. 1988. Harvard University Press. —Preceding unsigned comment added by 140.247.133.100 (talk) 23:58, 15 June 2008 (UTC)

Wrong... value?
I'm hesitant to change something so fundamental without asking others whether or not I'm crazy. Thirty-something years ago, in high school physics, I recall learning that the value of Planck's Constant was ~6.626e-34 Js, not ~6.636e-34 Js. Has this memory- like so many others- just failed? I know that this form is rarely actually used- honest-to-gosh physicists may not have noted the typo? Rt3368 (talk) 01:37, 15 January 2008 (UTC) I see that in the graphic under the heading "More recent values" that ~0.01e-34 has been subtracted from the first depicted value; this is probably correct.. Can someone check and change the first graphic, that appears as the first value under "Units, values and symbols"? Maybe check the values for the other forms depicted in the graphics as well? Rt3368 (talk) 01:49, 15 January 2008 (UTC)


 * You were right http://physics.nist.gov/cgi-bin/cuu/Value?h  I fixed it. It had been changed in this edit a few days ago. I added a reference so that anybody can easily check. /Pieter Kuiper (talk) 07:42, 15 January 2008 (UTC)

My intentions
Since User:Bo Jacoby insists after finding a minor error of mine among my many minor edits that I "state my intentions" on this page. I intend to continue to edit this article. You guys had five years to provide a clear explanation of what the Planck constant was and, in my opinion, you failed. This is difficult subject that requires a clarity of exposition that this article has lacked for many years. At least now the three equations relevant equations appear together and, thanks to one of my collaborators, we now have copious and appropriate references to the units of this constant: action (physics). So let's keep collaborating and step fretting about how many iterations it takes. I would rather you fret about how many years have past by with nobody getting this 50-year-old subject to be of use to those reader who do not yet already have a B.S. in Physics.--Truthnlove (talk) 21:38, 6 March 2008 (UTC)
 * Thank you. It may not be as easy as it sounds to provide a clear explanation, but good luck. This article should not be about everything related to Planck constant, because there are other articles about special subjects. The distinction between particles with mass and particles without mass is outside the scope. So is the distinction between elementary and composite particles, and between fermions and bosons. Bo Jacoby (talk) 10:29, 7 March 2008 (UTC).

Top of page
Would it not be a good idea to have the value of the constant in some suitably larger font at the top of the page? I just used wikipedia to look up the value of the constant myself, and for those in a hurry, would have made things much easier.

I'm sure the most important things people want to know about the constant is its value itself, and such a title value would give the page much more purpose. Perhaps an infobox would serve this purpose too?

92.1.90.36 (talk) 18:14, 29 April 2008 (UTC) Example: http://www.google.com/search?q=h this will display: Planck's constant = 6.626068 × 10-34 m2 kg / s"
 * No, when people only need the value of a constant, they ask Google.

 •ː•   3ICE   •ː•   11:42, 29 December 2008 (UTC)

Who calls it "Dirac's constant"?
I have been doing research and teaching in quantum mechanics for 20 years and I have never heard hbar called "Dirac's constant". Also I have never seen that usage in any standard textbook or review article. I tried googling it, and the only significant occurrence was in this wikipedia article! Please could someone supply reputable sources for this terminology? Dark Formal (talk) 18:58, 4 August 2008 (UTC)

Two weeks have passed and no one has shown that the term "Dirac's constant" is generally used or accepted. I will remove it from the article. Dark Formal (talk) 22:30, 18 August 2008 (UTC)


 * See http://www.scenta.co.uk/tcaep/nonxml/science/constant/details/dirac%27s%20constant.htm for example.Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 05:35, 8 December 2008 (UTC)

Firstly, that site is unreachable right now. But the criterion is generally used or accepted, i.e. does it have widespread use in standard physics media (mainstream journals, conference proceedings, standard textbooks, etc). I've never seen it used in any of those. Dark Formal (talk) 03:21, 15 December 2008 (UTC)

Needs expert attention
Here an alleged constant "changes", "tends to zero" and "is taken as 1" without the requisite explanation in terms of how Planck's relation holds at the quantum level.

Also, "Indeed, classical physics can essentially be defined as the limit of quantum mechanics as the Planck constant tends to zero", seems like the right idea misstated slightly, i.e. there's a useful aphorism hiding inside this misstatement, again in terms of Planck's relation.

Finally, explaining the reduced Planck's constant should be more cleanly separate from the explanation of quantization, as the reduction is only a matter of unit analysis not at all related to quantization.

Would like a coherent fix from someone who's taken physics more recently than I.

-SM 04:01, 6 December 2008 (UTC)


 * I've put a note that a comparison of classical mechanics and quantum mechanics in the LaGrangian/Hamiltonian formalisms would yield a lot of insight here, especially when it comes to Poisson brackets and commutators. I would make it myself, but I was unfortunately taught advanced classical mechanics by an utterly incompetent person, and I don't understand a thing about LaGrangian and Hamiltonian formalisms, and I do not trust what little I remember of them to be right due to said incompetence of the teacher.Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 05:33, 8 December 2008 (UTC)

OK, fair enough (and thanks for checking in on it), but I am thinking there is an even simpler explanation to make here. As it happens, I had a very good first-year Physics teacher, whom I am sure could make sense of this awkward, misleading (if well-intentioned) language without recourse to LaGrangian/Hamiltonian formalisms (and to whom I should have no doubt paid closer attention, or I'd be able to do it myself). The disconnects here are just too big for the introduction to an article this fundamental. -SM 13:53, 8 December 2008 (UTC)

Well I don't claim to be an expert here, but I think langage is extremely important here. Saying the its the behaviour as the limit when h &rarr; 0 looks a lot like someone said "take the limit h&rarr;0". I think, but cannot confirm, that this only makes sense in the LaGrangian/Hamiltonian formalisms. For example if you take the limit h&rarr;0 in the Plank relation, you get E=0, which doesn't make a lot of sense and certainly isn't classical behaviour. Many quantum operators have h (or hbar) in the operator and become meaningless if you take the limit h&rarr;0. However, if you say, classical behaviour is the asymptotical behaviour of things when h&rarr;0, then all relations remain meaningful and get closer to give classical descriptions of things, and you don't need advanced classical mechanics to give an intuitive image of quantization. I think, but cannot confirm, that oftentimes people say the limit h&rarr;0, when they actually mean the asymptotical behaviour as h&rarr;0. Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 21:46, 8 December 2008 (UTC)
 * Surely the point is not that E&rarr;0 as h&rarr;0, but that ΔE&rarr;0 as h&rarr;0, ΔE being the separation between possible energy levels. That's actually how Planck seems to see it in his original paper. Physchim62 (talk) 23:20, 8 December 2008 (UTC)

I'm glad to see everyone looking in on this. Having read the changes so far, I see a narrative which should tend (IMHO) towards this (formulae notional, please substitute better):
 * h is the proportion between the frequency and energy of a photon
 * h does not change
 * $$E = h\nu\,$$ (hertz)
 * $$E = \hbar\omega\,$$ (radians*hertz)
 * electrons in the orbital shells of atoms can only have certain energies
 * consequently atoms can only absorb and emit the energies of photons having certain frequencies
 * this is reflected in the absorption and emission spectra of different elements' atoms
 * this constrains the possible values of $$\nu\,$$ in $$E = h\nu\,$$
 * these narrow spectral bands in which light is absorbed/emitted reflects the small differences in possible energy, reflected in differences in color, and why h is measured in units so very small
 * h is very small, like photons, electrons and quanta
 * this is reflected in the units in which it is expressed
 * compare, for example, the energy of lifting one gram one centimeter (on Earth) and the corresponding (tiny) differences represented by lifting an electron from one shell to another, reflected in these frequency differences $$E = h(\nu\,2-\nu\,1)$$ and the mass of an electron.
 * this can be explored further in terms of frequency, angular momentum, etc.
 * this constant is determined by statistical sampling
 * this sampling has statistical uncertainty

I don't understand about h&rarr;0, or h changing at all (apart from sampling uncertainty), which may be my limitation, except the article says so, but doesn't explain why one would think of it this way. Specifically, I don't understand,


 * If the electron could have any indiscriminate energy – which would be the case if the Planck constant were zero, instead of just being very small compared to everyday human experience – the spectrum would be more like the one below.

None of it explains why h would change at all, as opposed to allowable $$\nu\,$$. Sorry if I am missing something obvious I should know.

-SM 12:39, 9 December 2008 (UTC)
 * No, the Planck constant doesn't change! Well, there are a few physicists, those who believe in VSL theory, who think it might have had a different value in the first few microseconds of the universe, but for all intents and purposes and in majority opinion, it is exactly what it says it is, a constant. The important point to get across is that it cannot be zero, otherwise physical equations start predicting silly things: a reductio ad absurdum.
 * The determination of the Planck constant is a whole story on its own, which really needs to be in the article but which I have never got round to writing up. Suffice it to say that it can be determined experimentally: Planck himself determined it to within 2.2% of the modern value. The CODATA value quoted in the article is the weighted mean of nine determinations by six different methods (from skimming the paper: don't quote me on that in the article; it could easily be, say, 16 measurements by five methods, if I'm reading things wrong, but you get the idea). The value of the Planck constant is also the "weak link" in our knowledge of the values of other physical constants, for example the Avogadro constant or the electron mass.
 * I think the next section for expansion is "Origins of the Planck constant". The historical story of Planck's postulate is quite instructive as to why h cannot be zero. On the other hand, I must admit that I can't see where the position–momentum communtator comes in at all: it seems to be trying to illustrate the importance of h in quantum mechanical formulation, but doesn't really do it for me… Physchim62 (talk) 13:21, 9 December 2008 (UTC)

I don't see why one would think of h ever being zero in the first place (having read to that point), or why it would lead to a continuous emission spectrum and no discrete quantum energy levels, or why making at that point a comparison of the size of the constant to everyday human experience has anything to do with absorption lines (the visible colors from which are part of everyday human experience).

I'm proposing rearranging the article into the order and progression of discrete steps in the outline above (simplifying as necessary to clarify the above points), but I don't know how/whether I would keep the zero-h idea. What do you think?

-SM 14:54, 9 December 2008 (UTC)
 * A very quick reply because I have to teach in 15 minutes time! h was assumed to be zero until Planck "invented" it! If there were no quantization, a hydrogen atom would behave in the same way as a black body (where quantization of the energy levels of the body is almost negligible). If you wish to reorder the article, be bold; this is a wiki after all. My concern is that the sum-total content of the article doesn't seem to be what I would want it to be. Physchim62 (talk) 15:22, 9 December 2008 (UTC)
 * I do (and did) understand,
 * The linear relation between wavelength and quantum energy levels are reflected in absorption spectra
 * If there were no quantization, a hydrogen atom would behave in the same way as a black body
 * ...but do not understand this in terms of,
 * h was assumed to be zero
 * h being zero implies black-body-like behaviour
 * I appreciate your patience, -SM 04:10, 11 December 2008 (UTC)
 * I hope my expansion of the history section sheds some light (quantized or not) on your queries! There's still some more work to do: I want to add a section on the photoelectric effect, for example, as Einstein's work was fundamental in convincing people that quantization was more than just a mathematical formalism. Physchim62 (talk) 15:07, 12 December 2008 (UTC)
 * its because the article is vastly incomplete and mixes several ideas. The E=hv does not apply directly to the hydrogen line spectrum (applying the lim(h->0) to this equation does not explain the line spectrum);


 * the reason the hydrogen spectrum has lines (and does not demonstrate black body like behaviour, or a complete spectrum) is because the electron in the hydrogen atom can only exist at discrete energy levels. the spectrum comes from the electron changing from one energy level to a lower one, emitting radiation. if there werent discrete energy levels, a hydrogen atom would show blackbody radiation. since there are only certain energy levels allowed, the transitions are discrete and it is a line spectrum (sorry for repeating myself so much, but sometimes its better to say things in a series of ways so people might catch one).


 * so how does this relate to planck: the energy of these discrete energy levels are explained using the debroglie hypothesis, which comes from combining planck's expression for energy (E=hv, describes a wave) with einstein's expression for energy (E=mc^2, describes a particle) to solve for energy of an electron in terms of frequency. It wasnt until the combination of wave/particle equations by debroglie that the hydrogen spectrum could be explained (it is not really complicated mathematically, dont need a degree to understand it). Since debroglie used planck's equation as a starting point, "h" is a constant throughout his work. Schroedinger's equation and Bohr theory (obsolete now) use debroglie's equation, and thus "h" is common throughout...


 * Solving schroedinger for energy or angular or total momentum show that they all are only possible in multiples of h. But the discrete spectrum of the hydrogen atom arises because there are discrete energy levels for the electrons. not because energy is quanitzed (although this has other ramifications). basically, the article is flawed. dont worry if you cant understand it. —Preceding unsigned comment added by 190.54.191.20 (talk) 14:01, 12 December 2008 (UTC)

removal of spectrum
i have removed the part about the hydrogen spectrum, since it was wrong. the hydrogen spectrum is a line spectrum because the electron can only occupy certain energy levels. While the possible energy states are multiples of h, it does not justify energy being quantized. if someone wants to readd it, it must be done so with at least discussion of debroglie's hypothesis, and the bohr model explaining orbitals/energy levels. the article needs a much heavier rewrite, but seeing something that is purely wrong warranted a quick removal IMO... —Preceding unsigned comment added by 190.54.191.20 (talk) 15:36, 12 December 2008 (UTC)
 * The difference between energy levels of a hydrogen atom is given by
 * $$\Delta E = {h}\frac{c_0R_{\infty}}{n^{\prime 2} - n^2} \,$$,
 * where n' and n are the principal quantum numbers of the two levels and R∞ is the Rydberg constant. That is the sense of the spectrum example: if the Planck constant were zero, there would be no spacing between energy levels and the hot hydrogen atom would behave as a black body. Of course, if the Planck constant were zero, the hydrogen atom couldn't exist as it would decay through Larmor radiation! But that's surely another story… Physchim62 (talk) 22:50, 12 December 2008 (UTC)
 * OK, now I get the whole "if h were zero" thing. Looking forward to reading all the work you've done on the article. (BTW, I'm not the unsigned guy at 190.54.191.20).  Thanks again, -SM 04:27, 14 December 2008 (UTC)


 * SM, be careful. the Rydberg constant includes the term 1/h^3, so if h->0 the energy term would approach infinity in your equation (see below, sorry not sure at how to use iwkipedia very well so had to edit several times).


 * $$\Delta E = \frac{2pi^2me^4}{h^2*(n^{\prime 2} - n^2)} \,$$


 * thanks for inserting the equation, i wanted to but was not sure how. From a mathematical POV, if you hold Rydberg's constant and just make the h in the numerator -> 0, blackbody radiation is the outcome but as you say doesnt mke sense. the article made it seem like quantization of light energy was the explanation for why hydrogen exhibits a line spectrum-- it is not. it is because there are discrete energy levels in which an electron can exist (if the n' and n didnt have to be integers in the equation, it would also not show a line spectrum). that is, if there were not discrete energy levels hydrogen would show blackbody radiation regardless of whether or not light was quantized.


 * the principle quantum numbers are the reason for the line spectrum. the fact that light energy exists in quanta is not an explanation for why there are electron orbitals... the real breakthrough of plancks work was realized by einstien and Bohr, the wave/particle duality, etc. either way, the hydrogen spectrum is a bad example.


 * —Preceding unsigned comment added by 190.54.191.20 (talk) 16:10, 15 December 2008 (UTC)

Too long!
Physchim62 is doing a lot of work on this article, and I am happy to see it is correct material clearly expressed. But the article is getting long and losing its focus. Wikipedia articles typically link to other articles rather than incorporating capsule summaries of them. Also, Physchim62, can you do a smaller number of larger edits instead of a large number of tiny edits? (ie larger quantum of editing!). It is easy to download the page, work on it for half an hour or so, and then upload the new version. It would make it easier to keep track of your changes if there are a few per day rather than hundreds. Dark Formal (talk) 03:30, 15 December 2008 (UTC)

Discrete vs. discontinuous
The end of the intro section previously said that energy must be discontinuous. Technically, this is true, but more specifically, it must be discrete. There are lots of ways it could be discontinuous - for example, it could be like the set of rational numbers. But the idea that energy comes in packets, or units, (like the intergers example correctly points out in the same sentence) is specifically tied to discreteness. --Jdvelasc (talk) 00:29, 7 February 2009 (UTC)

Why the Planck constant is written h ?
I understand that Planck himself wrote h. But for what reason h ? From the text of the wiki, I can make two hypothesis :

The hypothesis A looks more reasonable, but does someone know the true answer ? Of course, there is also the possibility that all other letters were already in use when he came to write his formula... --134.157.170.202 (talk) 14:42, 26 March 2009 (UTC)
 * A) h is for harmonic (oscillator)
 * B) h is for Humboldt (University)
 * As far as I know (and I've looked into it quite closely), nobody knows! I'm tempted to go with your third suggestion – that h happened to be a convenient letter that wasn't being used for anything else – but that would be mere speculation on my part! h also looks quite similar to k (at least in italic serif fonts), which Planck was using in the very same equations for what we now call the Boltzmann constant: maybe there was an element of esthetic appeal as well? Physchim62 (talk) 15:48, 26 March 2009 (UTC)

-- Probably just like the M-theory.. No one knows what the M stands for! XD Thγmφ (talk) 14:36, 16 April 2009 (UTC)

-- Membrane. 70.65.244.239 (talk) 20:15, 11 May 2011 (UTC)

Calculating the Planck constant
I understand that the Plank constant is ususally considered as a fundamental physical constant which cannot be calculated, but physics is still changing and this seems interesting.

Consider an electron falling in an atom. The potential energy of the electron is converted to kinetic energy, and I will assume this to be in the form of rotation around the atomic nucleus. The orbiting electron will radiate and dissipate its energy, and emit a foton (after some point the (Larmor?) radiated energy will equal the absorbed energy and the radiation will stop). Let's take the frequency of the foton to be determined by the time it takes for the electron to orbit the nucleus. Then we have: E = 1/2 m v^2

f = v / (2 pi r)

E = 1/(4 pi epsilon) q^2 / r (coloumb potential energy) Resulting in E = m^(1/2) q^(4/3) / (2 epsilon^(2/3) )  f^(2/3) This means that E is proportional to f^(2/3), but for visible ligth (f=10^15 Hz) one has,

E/f (f=10^15) = 9.8548E-34

and the Planck constant is: h=E/f = 6.62607e-34 The result is more or less acurate! At least in the right ballpark by decimal exponent. Any comments?

--Paclopes (talk) 19:31, 24 June 2009 (UTC)

--Corrected spelling and grammar, since I thought it was a very interesting point... I personally believe the planck constant can be calculated and see many analogies between quantum mechanics =?= (electromagnetism+dynamical systems)... although I dont see how the 4th equation results from the previous 3...

Why is frequency denoted by the letter "v"??
Seriously? In other articles frequency is denoted by the letter "f", while "v" is obviously velocity, this is confusing. Is this article correct? Aurora sword (talk) 13:18, 1 September 2009 (UTC)


 * It's not a v, it's the Greek letter ν (nu). This is very common usage.  Djr32 (talk) 18:14, 1 September 2009 (UTC)

Dirac's constant
A mention of "Dirac's constant" was removed with the comment. "hbar is not known as Dirac's constant. There is no "Dirac's constant". The Dirac's constant page should be deleted." Having done a Google search and found results which are not WP mirrors, I'd say there obviously is such a term, even if it doesn't see much use. Is half a sentence noting what this minor alternative refers to really too much? AlmostReadytoFly (talk) 08:43, 2 September 2009 (UTC)


 * Yes, it is too much. Those few pages are eccentric and unrepresentative. There is no reputable source (mainstream physics textbook or review article) that uses the term "Dirac's Constant". I have been a theoretical physicist doing research and teaching in quantum mechanics for over 20 years and I have never seen/heard the term used by any of my colleagues, or in any research paper or reputable book. Dark Formal (talk) 03:46, 3 September 2009 (UTC)


 * OK, I retreat. Stimulated by a web search by Aymatth2 I found that there are subfields of physics (outside field theory and particle physics) where this term is recognised. For example, Tony Leggett uses it. So I'm happy with mentioning it on this page. Dark Formal (talk) 22:14, 4 September 2009 (UTC)

Periods
Why are there periods at the end of the equations? Would that not confuse between punctuations in sentences with mathematical meanings? —Preceding unsigned comment added by 66.56.46.161 (talk) 04:53, 11 September 2009 (UTC)

Epic Fail ?!
The Planck constant (denoted h), also called Planck's constant(Epic Fail) —Preceding unsigned comment added by 204.19.10.199 (talk) 14:47, 20 November 2009 (UTC)

Intro (input)
Would it be clearer to add, "It is equal to the energy of a quantum of electromagnetic radiation divided by its frequency?" (That's how Oxford defines it.) I'm not an expert in this area, but although the value is in the table to the right of the intro, it seems like the simple explanation of how the constant is derived is missing. — DMCer ™  02:00, 12 January 2010 (UTC)

counterintuitivity
"This is counterintuitive in the everyday world, where it is possible to "make things a little bit hotter" or "move things a little bit faster", because the quanta of energy are very, very small in comparison to everyday human experience."

not true if one regards the right ratio - when dealing on this small degree of the scale dimension (which gets observed by only a small group to none in this world) and comparing it with the degrees of the scale dimension that are observed by many people of this world the ratio between a "small bit" and the whole on this "large scale" has to be the same as on the "small scale. And: it also makes it possible to predict limits on the large scale where most of the humans still think that there are no borders - they may directly look at them but not realizing them as being borders.

91.51.206.181 (talk) 18:47, 22 March 2010 (UTC)

Macroscopic significance
Could someone provide another macroscopic example other than "the energy of one mole of photons can be calculated by multiplying by the Avogadro constant, NA ≈ 6.022 × 1023 mol−1. Green light of wavelength 555 nm has an energy of 216 kJ/mol, equivalent to the strength of some types of chemical bond."? All this means is that it takes a mole of photons to break a mole of bonds, which doesn't seem to provide any insight into the Planck constant. Mwistey (talk) 07:00, 27 January 2010 (UTC)
 * The point of that example is that green light will break some types of chemical bonds, but not all types. Physchim62 (talk) 18:36, 28 January 2010 (UTC)
 * sure but then why elaborate on one mole of photons and bonds? it could just as well state that a single green photon can break some types of chemical bonds, but then this would not underline the "macroscopic significance". This section could almost be paraphrased as "lots of little things can cause lots of little reactions, which can be macroscopically observable" —Preceding unsigned comment added by 157.193.12.234 (talk) 19:43, 24 April 2011 (UTC)

Equation formatting?
I noticed that there is a period at the end of most of the equations in this article. Does this have mathematical meaning, or is it there for style reasons?

--Hroðulf (or Hrothulf) (Talk) 11:33, 10 June 2010 (UTC)
 * It seems odd to me, too. I would refer to eliminate those punctuation marks. Some books use punctuation marks after equations that are set off (not in-line), but only when they form a real sentence, e.g.,


 * The Planck relation or the Planck–Einstein equation is


 * $$E = h\nu.\,$$


 * but they do not use a punctuation mark after something like


 * ...the Planck relation or the Planck–Einstein equation:


 * $$E = h\nu$$


 * I think generally we do not punctuate after a long list, e.g,


 * Noah loaded on the ark:


 * Aardvarks
 * Zebras
 * Zebras


 * At the end of such a long list, "Zebras." would have people wondering what the punctuation mark is there for -- the same question I have when I see an equation on an isolated line followed by a period. Putting something on an isolated line is enough in itself. P0M (talk) 16:06, 30 October 2011 (UTC)

P0M (talk) 16:06, 30 October 2011 (UTC)

Why is Dirac's Constant introduced twice in the article?
The h-bar constant is introduced twice. WTF —Preceding unsigned comment added by 142.167.71.237 (talk) 01:35, 26 October 2010 (UTC)


 * Sure. This is because we summarize an article in its lead section.  See Manual of Style (lead section). --Hroðulf (or Hrothulf) (Talk) 18:46, 27 October 2010 (UTC)

Wien's formula
I think whoever wrote this has Wien's curve fit backwards?

"Wien made a guess for the spectrum of the object, which was correct at low frequencies (long wavelength) but not at high frequencies (short wavelength). It still wasn't clear why the spectrum of a hot object had the form that it has (see diagram)."

I think Wien's formula is a very good fit at HIGH frequencies / short wavelengths, and not so good at LOW frequencies / long wavelengths.

Thanks. BB —Preceding unsigned comment added by 24.149.122.74 (talk) 20:48, 22 November 2010 (UTC)


 * Yes, you are correct. It is explained properly in the article on the Wien approximation, where a reference is also given. I'll fix this article. Dirac66 (talk) 00:14, 23 November 2010 (UTC)

Error?
Not expert enough to do edit, but if I remember correctly it should be "time vs. energy", not "time vs. frequency". Frequency is simply inverse of time f = 1 / t. —Preceding unsigned comment added by 98.219.43.90 (talk) 06:32, 9 January 2011 (UTC)

Modification of Planck's constant in the research process
Unfortunately the article does not provide information about what value originally had Planck's constant immediately after the appearance of Planck's law - 6,55 x 10-34. Also during the research value of Planck's constant continuously increased. Probably such information should be included in this article. Leonid 2 (talk) 08:11, 12 May 2011 (UTC)
 * There's a good article from the Russian foundation for basic research - History refinement of Planck's constant (in Russian only without the English version). Can anyone make a selection in English for this article in Wikipedia. Leonid 2 (talk) 06:44, 18 May 2011 (UTC)