Elements of Classical and Quantum Physics pp 351-372 | Cite as

# Quantum Statistical Mechanics

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## Abstract

In general, the process that we use to prepare a system of atoms, molecules or whatever we want for a measurement produces many copies, but not all in the same quantum state. A where \(P_{n}\) is the (classical) probability of finding the system in \(\langle \psi _{n}|\).

*pure state*in which all the molecules, say, are in the same state, is a limiting case. In general, the system will be in a mixed state. One reason for that is that thermal excitations are unavoidable. Let the possible states be vectors of a Hilbert space with a basis \(\{\langle \psi _{n}|\}.\) The expectation value of an operator \(\hat{A}\) is$$ \langle \hat{A}\rangle =\sum _{n}P_{n}\langle \psi _{n}|\hat{A}|\psi _{n}\rangle ,$$

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