- #1
binbagsss
- 1,265
- 11
Homework Statement
Hi I have the following definition for the partition function of ##N## particles in ##s## dimensions:
I am looking at computing the partition function for this Hamiltonian:
The solution is here:
Homework Equations
above
The Attempt at a Solution
I don't understand the top line of this solution? The definition is to integrate over ##\Pi_{i=1}^{i=n} \Pi_{\alpha=1}^{\alpha=2}dP_{i,a}## not ##\Pi_{i=1}^{i=2N} d\vec P_i##
I can change to polar coordinates to get the integration over ##d\vec P_i## (just looking at the integration over ##P## and I have the same result, however in the first line of the solution there are no factors of ##2\pi## from the change of variables to polar coordinates, so how has the definition of the partition function been used? (or is it just by chance I've got the same answer)i.e. ##dP_x dP_y \neq d^2\vec P## does it?: