**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.

- Choice of Basis Vectors
- Replacement of Sums over All States with Sums over Eigenstates
- Quantum Effects on Classical Integrals
- Summary
- Problems
- References

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