Self-adjoint extensions in quantum mechanics : general theory and applications to Schrödinger and Dirac equations with singular potentials
Author(s)
Bibliographic Information
Self-adjoint extensions in quantum mechanics : general theory and applications to Schrödinger and Dirac equations with singular potentials
（Progress in mathematical physics / editors-in-chief, Anne Boutet de Monvel, Gerald Kaiser, v. 62）
Birkhäuser, c2012
Available at / 16 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
GIT||1||3200024911015
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Note
Includes bibliographical references (p. 497-503) and index
Description and Table of Contents
Description
This exposition is devoted to a consistent treatment of quantization problems, based on appealing to some nontrivial items of functional analysis concerning the theory of linear operators in Hilbert spaces. The authors begin by considering quantization problems in general, emphasizing the nontriviality of consistent operator construction by presenting paradoxes to the naive treatment. It then builds the necessary mathematical background following it by the theory of self-adjoint extensions. By considering several problems such as the one-dimensional Calogero problem, the Aharonov-Bohm problem, the problem of delta-like potentials and relativistic Coulomb problemIt then shows how quantization problems associated with correct definition of observables can be treated consistently for comparatively simple quantum-mechanical systems. In the end, related problems in quantum field theory are briefly introduced. This well-organized text is most suitable for students and post graduates interested in deepening their understanding of mathematical problems in quantum mechanics. However, scientists in mathematical and theoretical physics and mathematicians will also find it useful.
Table of Contents
Introduction.- Linear Operators in Hilbert Spaces.- Basics of Theory of s.a. Extensions of Symmetric Operators.- Differential Operators.- Spectral Analysis of s.a. Operators.- Free One-Dimensional Particle on an Interval.- One-Dimensional Particle in Potential Fields.- Schroedinger Operators with Exactly Solvable Potentials.- Dirac Operator with Coulomb Field.- Schroedinger and Dirac Operators with Aharonov-Bohm and Magnetic-Solenoid Fields.
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