Lecture 11 -- Formal Quantum Statistical Mechanics
This Lecture applies the general quantum-mechanical principles developed in Lecture 10 to analyze the statistical mechanics of quantum-mechanical systems. The analysis is in two parts. The first, more conventional, part will show why a sum over energy eigenstates is an appropriate procedure for evaluating ensemble averages, but why the choice of basis vectors has no effect on the numbers obtained from the average. The second, less conventional, part of the discussion will elaborate on the distinction between a complete set of all possible states of the system and a complete set of basis vectors. It will be shown that ensemble averages over the set of all states and over the set of all basis vectors give the same answer. We'll also note how quantum mechanics evaluates the floating constant C which has appeared in ensemble averages.