January 25th, 2012

Hard life of my students. Statistics for bosons.

If you deal with bosons then you don't have to take into the account the principle of Pauli's exclusion. The particles are indistinguishable, so probabilities for all the states are just one. But to calculate the average energy at T=const one has to  write a partition function which is something like: Z=Sum_{E_k}e^{-\beta E_k} = .... (considering each degeneracy case...)
= -\epsilon*3*\frac{sinh(3\beta\epsilon)+sinh(\beta\epsilon)}{cosh(3\beta\epsilon)+(cosh{\beta\epsilon)} (more or less LaTeX text).

This is however not easy to calculate, especially analytically :)

This is what my students wrote while doing this exercise:

"Somehow it is not possible to plot this function. Looks constant."

"Sorry, I cannot continue anymore..."

"Z=....something weird..."

"Z=long hard derivations; since the task is for 1 point only, I rather skip this part..."

Nice students! I think I'll kill them tomorrow.
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