Talk:Density of states

Density of states
I regrouped together the topics of this Talk pages that seem to refer to the same topic in the Article, and used to be scattered all over. To improve readability of comments, I also 'blockquoted' relevant part of the text in two posts (from source clearly quoted from the Article; but was not easily evident what was quoted while reading talk pages before). It seems people who added the following comments didn't return here, but this Article needs work on. For now, I didn't dare to do more than edit the text in Talk pages. --Marjan Tomki SI (talk) 16:12, 14 April 2020 (UTC)

Question to the writer of the section before Introduction.
"In general a DOS is an average over the space and time domains occupied by the system." Average of what??? wave function of the system? 91.154.126.87 (talk) 15:34, 26 February 2013 (UTC)

Hard to understand generalization
"Unlike isolated systems, like atoms or molecules in gas phase, the density distributions are not discrete like a spectral density but continuous."

(1) Why would atoms and molecules in a gas phase have a discrete density of states?

(2) Is the author of this sentence possibly using the notion of "isolated system" too narrowly, perhaps referring to systems that studied and named in the literature? Presumably any system can be made isolated by isolating it.

(3) What is the opposite of an isolated system? A well-defined, thermodynamic model system connected to a heat bath? Or any not-isolated portion of any system?

89.217.0.204 (talk) 12:46, 6 February 2015 (UTC)

Too limited definition
I propose to start out with the more general definition of the density of states for a quantum system: $$\nu(E) = \sum_{n} \delta(E-E_n),$$ where $$E_n$$ are the energy levels (eigenvalues of the Hamiltonian) of the system. IMO this is much easier to understand, since the reader need only be familiar with the very basic properties of a quantum system.

Later in the article one can present the density of states for a crystalline system. Here one will need to introduce (or at least mention) reciprocal space and other topics that require familiarity with solid state physics. —Preceding unsigned comment added by Havard.haugen (talk • contribs) 10:02, 14 January 2008 (UTC)

Defining DOS as a histogram.
If I am wrong, one can define the DOS in in the following simple way: "the histogram of energy levels" or "histogram of the eigenenergies". I think that It is a good idea to put this simple definition in the beginning of the article. I can imagine this could help, for example, undergrad students grasp the main point of the DOS thing. Condmatstrel (talk) 21:17, 15 June 2011 (UTC)

Part of disputed piece of text has been changed since then
This is what I found now. "Generally, the density of states of matter is continuous. In isolated systems however, such as atoms or molecules in the gas phase, the density distribution is discrete, like a spectral density. Local variations, most often due to distortions of the original system, are often called local density of states (LDOS)." The piece I 'bolded' still seems to be unclear in several ways(as also seen also from two opinions I now moved together). So: At that level of detail (quantum) I surely can't rely on my 'common sense of macro world', where we don't experience quanta effects (because our biological info systems do aggregation, averaging and so on, without most of us being aware of that). So I also can't rely on my (macro) common sense about probabilities in quanta world being continuous; I would like to see references to sources (could be in wikipedia) that statement is based on and - if possible - to be able to have it traced to the experiments) showing it to be so - or not to be so. So anybody knows who determined that (etc.)? --Marjan Tomki SI (talk) 16:12, 14 April 2020 (UTC)
 * 1) I am not sure what 'Generally' should mean in this context (in 'incarnation' cited above it might have meant 'taken as average for volume of interest or measure', but is really undefined).
 * 2) Original author might have in mind that DOS is variable, when looked in detail, but was somehow taken just with average as represented for an aggregate previously (ten years ago possibly before tools were available or being used for detailed data to be acquired? - if so I would be interested in a link to a source with stry on how and why it was so)
 * 3) I also can't see where I can check if the 'bolded' statement about  continuous and/or discrete of actual property of matter (not just of possibility of it being measured) can be checked if it is true or not.

Connection to entropy
I have added a simple sentence stating the connection of the density of states to entropy. Maybe someone more familiar with the condensed matter point of view can expand this. Jorgenumata (talk) 19:59, 16 February 2008 (UTC)


 * It seems that this sentence didn't survive a large edit made recently. Any discussion of this topic is incomplete without discussing entropy (from my viewpoint entropy is the only reason to even talk about the density of states).  Man It&#39;s So Loud In Here (talk) 19:32, 9 March 2008 (UTC)

experimental measures
Can someone who knows a bit about this stuff add a section on how the density of states can be experimentally measured? Thanks 137.222.30.62 (talk) 16:44, 15 June 2010 (UTC) I would use positron annihilation and or electron energy loss spectroscopy or XPS all these techniques are featured in Wikipaedia —Preceding unsigned comment added by 143.167.129.251 (talk) 08:43, 20 July 2010 (UTC) As far as I see one of means seem to be by scanning tuneling microscope and this link could be part of such a section. In X-ray photoelectron spectroscopy/Uses and capabilities I find mention of The density of electronic states, but IMO that should be worked on before it could be useful for general public. For positron annihilation spectroscopy the page seem to be stub-like and I didn't see DOS mentioned; if it can measure DOS, that article should be expanded accordingly. But edit of the actual Article (this or those on links I mentioned) should be done by somebody that actually works with these things, not by me only trying to understand the results reported by others at the moment. --Marjan Tomki SI (talk) 16:12, 14 April 2020 (UTC)

Figure 2 is the third figure
...which makes me wonder if the text and figure were copied (possibly inappropriately) from another source, e.g. a textbook? Can someone include inline cites for that material? —Preceding unsigned comment added by 128.163.128.193 (talk) 17:47, 22 July 2010 (UTC) Also there are two "Figure 2"s, thus the reference in the introduction is misleading. —Preceding unsigned comment added by 193.174.238.115 (talk) 14:18, 10 March 2011 (UTC)

Dispersion relations
In solid states physics $$k_F$$ is commonly used as symbol for the fermi-wave-vector. This might lead to misunderstandings. In the context of inter-atomic forces D is often used. SolidStateDD (talk) 15:04, 10 March 2011 (UTC)

General calculation of DOS
There is always a way to calculate the DOS for systems with a complicated dispersion (esp. with multi band dispersions with non quadratic / linear relationships, by application of the formula:

$\rho(\omega)=\int\delta(\omega - \omega_k)$

with $\omega_k$ the $k$ dependant dispersion of the system of interest. — Preceding unsigned comment added by 77.100.221.252 (talk) 22:50, 3 July 2011 (UTC)

symmetry and density of states
The line says "Angular dependent calculations or measurements on a systems consisting of a single crystal of a compound, for example, are not anisotropic. " Should this not be "are anisotropic" or "are not isotropic"? I don't want to make changes without vetting them, but this seems clearly a typo.129.118.128.128 (talk) 18:27, 17 August 2011 (UTC)

No explicit formulae
This page has no explicit formulae for the DOS, even for simple particle in a box/surface/well/quantum dot. I would like to add this section with derivations similar to this page (http://britneyspears.ac/physics/dos/dos.htm). Would this be considered a useful addition?Larryisgood (talk) 13:31, 3 April 2013 (UTC)

Reference to the microcanonical partition function is missing
Reference to the microcanonical partition function is missing--Biggerj1 (talk) 22:14, 5 March 2014 (UTC)

Easiest definition missing?
I think the easiest definition of the density of (quantized) states by far,
 * $$D(E) = \sum_{k} \delta(E - E(k))$$

is missing here. $$k$$ is a stand-in for any indices you may need, e.g. $$k \rightarrow (\sigma, \vec k)$$ for electrons. I like this one the best because a) it follows directly from the words "density of states" and b) by rewriting the sum as an integral and plugging in your dispersion relation, you arrive directly at the results given in the article by simply evaluating the integral. It might not be as pedagogical as the others but I think it should be somewhere in the article. --92.211.105.220 (talk) 21:50, 7 September 2016 (UTC)

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Figure 4 gives a wrong graph
The green line is not a product of the DOS and fermi-dirac distribution; the DOS function should be shifted so that its zero (both for holes and electrons) lines up with the zero of the product (green) function. 137.120.234.19 (talk) 14:51, 2 July 2017 (UTC)

Missing the relation to volume?
I don't see anywhere in this page the fact that DOS is the number of allowed states per unit energy *per unit volume*.

At the very beginning this fact is omitted: "the density of states (DOS) of a system describes the number of states per an interval of energy at each energy level available to be occupied."

This is a fundamental part of the definition of the DOS and it appears to be missing. — Preceding unsigned comment added by 70.68.81.41 (talk) 20:46, 22 January 2019 (UTC)

"Optics and photonics" section needs secondary or textbook sources.
The section on "Optics and photonics" is confusing and incorrect. It relies on primary refs that are not properly summarized; I don't think they support the section either. The primary refs are very detailed studies, not summaries of the relation between local density of states and photonics.

I add a nag-tag to the section. Johnjbarton (talk) 15:14, 16 March 2024 (UTC)