Talk:Bose–Einstein statistics

First plot (distributions) is wrong

For bosons, $\epsilon _{i}\geq \mu$ $\forall i$. If $T$ is in Kelvin, so that $T\geq 0$, there cannot be a region in the plot where $(\epsilon _{i}-\mu )/kT<0$.

Untitled

"The quantum concentration is when..." doesn't sound like good english. Anybody knows what should be written there? 67.180.29.122 02:56, 5 November 2007 (UTC)

OK, I have changed it to a construction using "the quantum concentration, for which ...". This was a very tricky edit, since the offending sentence was not in the source code to be edited. I realized that the article uses Template:Physics/ParticleDistributions which is used to place the identical text in the 3 articles on B-E, F-D and M-B distributions. So I corrected the template (and made some other English corrections as well) so that all 3 articles would be corrected simultaneously. In theory at least - in practice I also had to purge the cache for 2 of the 3 articles following instructions in WP:Purge. Not simple but now it is done. Dirac66 (talk) 04:07, 4 January 2009 (UTC)

Distribution Graph

Is there any chance of putting a graph of the distribution in the same way as the one in the fermi-dirac statistics page? Grj23 14:45, 9 February 2007 (UTC)

Can model it after based on ${\bar {n}}_{i}={\frac {1}{e^{(\epsilon _{i}-\mu )/kT}+1}}$. The only difference with the B-E distribution should be the factor of $g_{i}$ and the $-$ in the denominator: $n_{i}={\frac {g_{i}}{e^{(\varepsilon _{i}-\mu )/kT}-1}}$ TSchwenn (talk) 21:30, 26 March 2012 (UTC)

Distribution formula missing?

The distribution formula appears to be missing. --Andreas Rejbrand (talk) 12:42, 16 November 2008 (UTC)

Chemical potential=0 - an extra description for BEC

I have a suggestion for adding an useful writting in an article. Write chemical potential equals to zero when undergoes BEC. We know that the critical temperature. When T is much smaller than that, BEC happens. —Preceding unsigned comment added by 210.66.168.3 (talk) 15:07, 26 November 2009 (UTC)

Not Exactly

Actually, the chemical potential its that it can be approximated to be zero not that it equals zero. If you read pages 200 -202 of Thermal Physics by Charles Kittel, Kittel points out that "The chemical potential of a boson system must always be lower in energy than the ground state orbital in order that the occupancy of every orbital be nonnegative". ( Note: Kittel uses λ = absolute activation energy, where λ = exp(μ/T) ) In other words he saying chemical potential has nonzero energy; however, for the orbitals to not have a negative number of particles, chemical potential energy must be less than the ground state energy at temperature = 0. He also later goes on to give an example when the chemical potential may be negligible. If you continue read up to page 205, Kittel not only shows that the chemical potential is not negligible for finding the number of particles in ground state orbital, but actually shows how you can still derive the Bose-Einstein Condensation temperature. Physics16 (talk) 14:46, 16 June 2010 (UTC)

Kittel is a rather basic text covering solid state physics, where Helmholtz energy is approximated by the Fermi energy. If you are relying on this book for your authority on general statistical mechanics and thermostatistics, then this is problematic.Wikibearwithme (talk) 18:21, 16 January 2016 (UTC)

Strange inclusion

The article currently says:

1. Why "{3 + 4 - 1 \choose 3-1}"="{3 + 4 - 1 \choose 4}"? I Think you should write "\choose 3+1" instead of "\choose 3-1"

This material appears to be some reader's critique, and should not be included in the article itself, no? P0M (talk) 04:08, 9 February 2012 (UTC)

No, it doesn't belong in the article. Whoever wrote it seems to think there is a mistake in a formula, and is suggesting a correction. But the formula is okay: the multiset coefficient ((3 4)) is, by definition, equal both to ( 3+4-1 choose 3-1 ) and to ( 3+4-1 choose 4 ). In general, ((n k)) = ( n+k-1 choose n-1 ) = ( n+k-1 choose k ). I suppose one could object, though, to the fact multiset coefficients are denoted here with angle brackets, but on the Wikipedia page on multiset coefficients to which a reference is given, double parentheses are used instead. Phorse (talk) 22:23, 14 March 2012 (UTC)

Bose did not develop the distribution for "bosons", Planck did

The notion that the BE distribution is different than that of the Planck distribution, or that it was the breaking proposal for quantization of EM radiation, is a fiction for those who apparently need to glorify Bose, as is done in the whimsical history that is opening this article. The only aspect that substantially differentiates the BE distribution, as other than a rather redundant restatement of Planck's distribution as probabilities of state, was the addition of the chem potential by Einstein (similar to the concomitant FD statistics), as well as Einstein's extension to atoms, and Einstein's prediction of the condensate, which, contrary to this article, was not done "in collaboration" with Bose - it was developed and published independently by Einstein. That's just the historical record.

As far as the propagated fantasy that Bose introduced the quantization theory of photons, anybody can easily confirm that this is completely untrue by consulting the much earlier work by Planck (e.g., "The Theory of Heat Radiation," Planck, published 1914, is his own review of his earlier work and is readily available). Compton's experimental work and publication, 23 years after Planck's work on this, in 1923 (still before Bose's paper) on the particle-like attributes of x-rays, was then considered to be the most convincing experimental verification of this, at that point, long-standing assertion on the quantum nature of light. Wikibearwithme (talk) 18:30, 16 January 2016 (UTC)

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What about Superconductivity -- ? --

Currently (as of the "Latest revision as of 03:27, 27 August 2024" version of this article), the second sentence of this article says [QUOTE]:

The aggregation of particles in the same state, which is a characteristic of particles obeying Bose–Einstein statistics, accounts for the cohesive streaming of laser light and the frictionless creeping of superfluid helium.

. Should that list -- (where each list entry has a wikilink to another Wikipedia article) -- be extended (to also include Superconductivity) -- ? --

I am not saying it should; ... just asking. Mike Schwartz (talk) 20:21, 8 September 2024 (UTC)