Path integrals in quantum mechanics / Jean Zinn-Justin.

Format:

Book

Author/Creator:

Zinn-Justin, Jean.

Series:

Oxford graduate texts.

Oxford graduate texts

Language:

English

Subjects (All):

Path integrals.

Quantum theory.

Physical Description:

1 online resource (xiii, 320 p. ) ill.

Place of Publication:

Oxford : Oxford University Press, 2010.

Summary:

The goal of this book is to introduce students to path integrals within the context of ordinary quantum mechanics and non-relativistic many-body theory, before facing the problems associated with the more involved quantum field theory formalism. The main goal of this work is to familiarize the reader with a tool, the path integral, that offers an alternative point of view on quantum mechanics, but more important, under a generalized form, has become the key to a deeper understanding of quantum field theory and its applications, which extend from particle physics to phase transitions or properties of quantum gases.Path integrals are mathematical objects that can be considered as generalizations to an infinite number of variables, represented by paths, of usual integrals. They share the algebraic properties of usual integrals, but have new properties from the viewpoint of analysis. Path integrals are powerful tools for the study of quantum mechanics, because they emphasize very explicitly the correspondence between classical and quantum mechanics. Physical quantities are expressed as averages over all possible paths but, in the semi-classical limit, the leading contributions come from paths close to classical paths. Thus, path integrals lead to an intuitive understanding and simple calculations of physical quantities in the semi-classical limit. We will illustrate this observation with scattering processes, spectral properties or barrier penetration.The formulation of quantum mechanics based on path integrals, if it seems mathematically more complicated than the usual formulation based on partial differential equations, is well adapted to systems with many degrees of freedom, where a formalism of Schrodinger type is much less useful. It allows a simple construction of a many-body theory both for bosons and fermions.

Contents:

1. Gaussian integrals; 2. Path integral in quantum mechanics; 3. Partition function and spectrum; 4. Classical and quantum statistical physics; 5. Path integrals and quantization; 6. Path integral and holomorphic formalism; 7. Path integrals: fermions; 8. Barrier penetration: semi-classical approximation; 9. Quantum evolution and scattering matrix; 10. Path integrals in phase space; QUANTUM MECHANICS: MINIMAL BACKGROUND; A1 Hilbert space and operators; A2 Quantum evolution, symmetries and density matrix; A3 Position and momentum. Scrodinger equation

Notes:

Originally published: 2005.

Formerly CIP.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed October 10, 2013).

ISBN:

9780191581427

0-19-158142-9