Talk:Gas in a harmonic trap

Error in formula
Potential error: in the expression for $$dg$$, the $$\beta^3$$ should cancel. Perhaps this was miscopied? (I don't have the necessary information myself, it just seems like an error)


 * You are right, it does cancel, but its not cancelled so that its easier to integrate. &beta;E is dimensionless, so its carried along without cancelling. PAR 05:42, 30 November 2005 (UTC)

Alright, that makes sense. New problem: For $$N = \frac{f}{(\hbar\omega\beta_c)^3}~\frac{1}{2}~\zeta(3)$$, I think that factor of 1/2 should disappear. $$\int_0^\infty \frac{x^2}{e^x-1} dx = 2 \zeta (3)$$, or so Mathematica tells me. --Keflavich 02:33, 1 December 2005 (UTC)


 * Thats right, and I have fixed it. Thank you for pointing that out. It's been a while since I wrote that article, so I fixed it by correcting the math, but that kind of thing worries me. Please, check the corrections I have made and, while reading this article, be on the lookout for any other errors. If you find them, please let me know. Thanks - PAR 05:01, 1 December 2005 (UTC)


 * That's all I noticed when I was going through it. However, it might be worth defining $$g_0$$.  In the text I'm using, Kittel/Kromer (I don't have the full cite handy b/c I'm using a photocopy), they use the equation $$N_0(\tau)=\frac{1}{\lambda^{-1}-1}=\frac{z}{1-z}$$ (the third expression is my own, translating from lambda to z).  They specify that it is for the orbital at $$\epsilon=0$$.  Since g is defined as the number of states with energy less than E, should $$g_0$$ just be defined to be 1? --Keflavich 21:05, 1 December 2005 (UTC)

It makes sense, but the "tacking on" of the ground state is an approximation. I'm not sure about g0=1, so I would rather leave it. With regard to defining it, yes, it needs a little explanation, and I will do that. Thanks - PAR 04:28, 2 December 2005 (UTC)

In discussing Massive Bose-Einstein particles in the sentence:
 * "Where Lis(z) is the polylogarithm function. The polylogarithm term must always be positive and real, which means its value will go from 0 to $$\zeta(3/2)$$ as z goes from 0 to 1."

Shouldn't Lis(z) go from 0 to $$\zeta(3)$$ not $$\zeta(3/2)$$?


 * That's right. I fixed it, thank you. The 3/2 is for a gas in a box, and I believe I copied the section from that article, and then altered the value of the exponent, and that was one I missed. PAR 21:21, 17 January 2006 (UTC)

The harmonic trapping potential is not listed.
I came here for the form of the harmonic trapping potential. It is not on the page or linked to from the page. Since I don't know it myself I cannot add a section on it, but for future readers it would be best to list an equation describing the harmonic trapping potential. — Preceding unsigned comment added by Whole Oats (talk • contribs) 23:18, 15 March 2022 (UTC)