Oxford University Press eBooks

Basic Tools For Quantum Mechanics

Robert Alicki, M. Fannes

Published Jul 12, 2001• 0 citations

Abstract

This chapter reminds, without entering into details, the main mathematical concepts and results relevant for finite system quantum mechanics. The basic postulates single out a Hilbert space of wave functions with self-adjoint linear operators corresponding to observables as was originally discovered by von Neumann. The chapter connects the contemporary terminology of linear Hilbert space operators with quantum physics. Important concepts like linear operators, measures, self-adjointness, spectral measures, density matrices, and tensor products are discussed and illustrated in the light of observables, probability for quantum systems and composite systems. A first example of a useful algebra of observables, the Weyl algebra, is described in detail and linked to the classical phase space of a point particle.

DOI: 10.1093/acprof:oso/9780198504009.003.0002

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