Chapter

Quantum Theory

Jochen Rau

in Statistical Physics and Thermodynamics

Published in print September 2017 | ISBN: 9780199595068
Published online November 2017 | e-ISBN: 9780191844300 | DOI: https://dx.doi.org/10.1093/oso/9780199595068.003.0002
Quantum Theory

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From the outset statistical mechanics will be framed in the language of quantum theory. The typical macroscopic system is composed of multiple constituents, and hence described in some many-particle Hilbert space. In general, not much is known about such a system, certainly not the precise preparation of all its microscopic details. Thus, its description requires a more general notion of a quantum state, a so-called mixed state. This chapter begins with a brief review of the basic axioms of quantum theory regarding observables, pure states, measurements, and time evolution. Particular attention is paid to the use of projection operators and to the most elementary quantum system, a two-level system. The chapter then motivates the introduction of mixed states and examines in detail their mathematical representation and properties. It also dwells on the description of composite systems, introducing, in particular, the notions of statistical independence and correlations.

Keywords: quantum theory; projection operator; two-level system; mixed state; composite system; statistical indepence; correlations

Chapter.  7476 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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