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Quantum Dynamical Systems$
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Robert Alicki and Mark Fannes

Print publication date: 2001

Print ISBN-13: 9780198504009

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780198504009.001.0001

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Basic Tools For Quantum Mechanics

Basic Tools For Quantum Mechanics

Chapter:
(p.4) 2 Basic Tools For Quantum Mechanics
Source:
Quantum Dynamical Systems
Author(s):

Robert Alicki

Mark Fannes

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198504009.003.0002

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.

Keywords:   Hilbert space, self-adjoint operator, spectral measure, observable, quantum probability, density matrix, tensor product, Weyl algebra

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