Path Integrals in Quantum Mechanics
Series: Oxford Graduate Texts;
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Product details:
- Publisher OUP Oxford
- Date of Publication 8 July 2010
- ISBN 9780198566755
- Binding Paperback
- No. of pages336 pages
- Size 241x168x18 mm
- Weight 560 g
- Language English
- Illustrations 20 b/w line illustrations 0
Categories
Short description:
Quantum field theory is hardly comprehensible without path integrals: the goal of this book is to introduce students to this topic 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.
MoreLong description:
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 Schrödinger type is much less useful. It allows a simple construction of a many-body theory both for bosons and fermions.
... an exceptionally clear and thorough book ... should be about as good a book on the subject as one could imagine.
Table of Contents:
Gaussian integrals
Path integral in quantum mechanics
Partition function and spectrum
Classical and quantum statistical physics
Path integrals and quantization
Path integral and holomorphic formalism
Path integrals: fermions
Barrier penetration: semi-classical approximation
Quantum evolution and scattering matrix
Path integrals in phase space
Quantum mechanics: minimal background
Hilbert space and operators
Quantum evolution, symmetries and density matrix
Position and momentum. Scrödinger equation
