Prove Van Leeuwen's Theorem: Diamagnetism Does Not Exist in Classical Physics

[Henk]

For a statistical mechanics course we have to prove Van Leeuwen's theorem: Diamagnetism does not exist in classical physics.

I know that in an external magnetic field H the Hamiltonian Ha goes from Ha(p1,p2,--------,pN ,q1,q2,-------qN) to Ha(p1-(e/c)A1, p2-(e/c)A2, ------- pN-(e/c)AN, q1,q2,------.qN)

I also know that the induced magnetization M = kT*d(log QN)/dH

So the problem is finding QN. I know how to calculate it for a perfect gas without the magnetic field but I can't seem to solve the integral when Ha changes.

 

[Physics Monkey]

Try shifting integration variables.

 

[Henk]

Ah I found bij changing p - (e/c)A to p' and then integrating. Thanks a lot.