Statistical mechanics - density of states

[ehudhaim]

Hi,
I'm studying statistical mechanics from Reif's book.
In his book Reif is reaching the conclusion that the number of states avaiable to a system at energy E (up to some small uncertainty in the energy due to finite observation) with f degrees of freedom is proportional to E^f .
There is a "not so much" of a proof of this lemma in his book, he assumes many things in that so called proof.
could anyone please refer me to an exact proof?
By the way, I did an introductionary course in qunatum physics so feel about free to refer me to formal proofs.

Another small question: Does the "a-priori probability" theorem in quantum statistical mechanics comes directly from Von Neumann's equation? Or do I have to postulate something else?

Thank you very much for helping. I am sorry for my bad english.
Ehud.

 

[BigJDubs]

The proof of Reif's lemma can be found in many textbooks on statistical mechanics. A good reference is the book "Statistical Mechanics: Theory and Molecular Simulations" by David Chandler, which provides a rigorous proof of the lemma. The "a priori probability" theorem in quantum statistical mechanics is derived from the Von Neumann equation, which describes how an isolated quantum system evolves in time. This equation provides the basis for deriving the Boltzmann distribution, which gives the probability of a system being in a particular state given its energy.