Quantum Statistical Mechanics

  • Michele Cini
Part of the UNITEXT for Physics book series (UNITEXTPH)


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 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
$$ \langle \hat{A}\rangle =\sum _{n}P_{n}\langle \psi _{n}|\hat{A}|\psi _{n}\rangle ,$$
where \(P_{n}\) is the (classical) probability of finding the system in \(\langle \psi _{n}|\).

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Università di Roma Tor VergataRomeItaly

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