1
vote
2answers
465 views

Confusion about Free Energy and the Hamiltonian

I'm probably making a relatively basic mistake here, but I'm a bit confused about the relation between the Hamiltonian and Helmholtz free energy. From what I can see, the free energy can be written ...
1
vote
1answer
155 views

Quantum Stat-Mech Proof of an Inequality for the Partition Function

I have the following problem that I was unable to solve for class, but I had a couple first steps that I started with that I am unable to finish. I know I can't get this since it's already been ...
5
votes
3answers
696 views

What is the relationship between Schrödinger equation and Boltzmann equation?

The Schrödinger equation in its variants for many particle systems gives the full time evolution of the system. Likewise, the Boltzmann equation is often the starting point in classical gas dynamics. ...