# Thermal wavelength and critical temperature for Bose-Einstein condensate

I'm stuck with derivation of critical temperature and thermal wavelength for Bose-Einstein condensate - all sources describe equations very briefly. Suppose we have a system described by Bose-Einstein statistics - its de Broglie wavelength, taken from mean energy, will be:

$$kT_c=\frac{2\pi\hbar^2}m\Big(\frac{N/V}{\zeta(3/2)}\Big)^{2/3}$$

and, according to this, critical wavelength will be:

$$\lambda_c=\sqrt{\frac{2\pi\hbar^2}{mkT_c}}=\zeta(3/2)^{1/3}\frac1{(N/V)^{1/3}}.$$

I've got equations from this source, but I still can't find even the handbook which would give fair enough derivation of de Broglie thermal wavelength, not to mention derivation of critical temperature. It would be great, if somebody here would give a proper answer.

• Take a look at pages 194 and 195 of Kardar's book. It is a wonderful textbook in graduate school. You can refer to earlier sections if you see the need:home.basu.ac.ir/~psu/Books/… – Benjamin Mar 19 '16 at 18:54