Path Integrals in Quantum Mechanics

Paperback | September 1, 2010

byJean Zinn-Justin

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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, whichextend 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-classicallimit. 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 allowsa simple construction of a many-body theory both for bosons and fermions.

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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, whichextend from particle physics to phase transi...

Professor Jean Zinn-Justin is Head of Department at Dapnia, CEA/Saclay, France.

other books by Jean Zinn-Justin

Format:PaperbackDimensions:336 pages, 9.45 × 6.61 × 0.07 inPublished:September 1, 2010Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198566751

ISBN - 13:9780198566755

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Table of Contents

1. Gaussian integrals2. Path integral in quantum mechanics3. Partition function and spectrum4. Classical and quantum statistical physics5. Path integrals and quantization6. Path integral and holomorphic formalism7. Path integrals: fermions8. Barrier penetration: semi-classical approximation9. Quantum evolution and scattering matrix10. Path integrals in phase spaceQuantum mechanics: minimal backgroundA1. Hilbert space and operatorsA2. Quantum evolution, symmetries and density matrixA3. Position and momentum. Scrodinger equation

Editorial Reviews

"... very well written ... and not only pedagogically useful, but also useful to the experienced practitioner." --Randall Kamien, University of Pennsylvania