Self-adjoint extensions in quantum mechanics : general theory and applications to Schrödinger and Dirac equations with singular potentials

The Resource Self-adjoint extensions in quantum mechanics : general theory and applications to Schrödinger and Dirac equations with singular potentials
Label
Self-adjoint extensions in quantum mechanics : general theory and applications to Schrödinger and Dirac equations with singular potentials
Title remainder
general theory and applications to Schrödinger and Dirac equations with singular potentials
Statement of responsibility
D.M. Gitman, I.V. Tyutin, B.L. Voronov
Creator
Contributor
Subject
Language
eng
Summary
Quantization of physical systems requires a correct definition of quantum-mechanical observables, such as the Hamiltonian, momentum, etc., as self-adjoint operators in appropriate Hilbert spaces and their spectral analysis. Though a?naïve? treatment exists for dealing with such problems, it is based on finite-dimensional algebra or even infinite-dimensional algebra with bounded operators, resulting in paradoxes and inaccuracies. A proper treatment of these problems requires invoking certain nontrivial notions and theorems from functional analysis concerning the theory of unbounded self-adjoint operators and the theory of self-adjoint extensions of symmetric operators. Self-adjoint Extensions in Quantum Mechanics begins by considering quantization problems in general, emphasizing the nontriviality of consistent operator construction by presenting paradoxes of the naïve treatment. The necessary mathematical background is then built by developing the theory of self-adjoint extensions. Through examination of various quantum-mechanical systems, the authors show how quantization problems associated with the correct definition of observables and their spectral analysis can be treated consistently for comparatively simple quantum-mechanical systems. Systems that are examined include free particles on an interval, particles in a number of potential fields including delta-like potentials, the one-dimensional Calogero problem, the Aharonov-Bohm problem, and the relativistic Coulomb problem. This well-organized text is most suitable for graduate students and postgraduates interested in deepening their understanding of mathematical problems in quantum mechanics beyond the scope of those treated in standard textbooks. The book may also serve as a useful resource for mathematicians and researchers in mathematical and theoretical physics
Member of
Cataloging source
GW5XE
Dewey number
530.1201/51
Index
index present
Language note
English
LC call number
QC174.17.M35
LC item number
G58 2012
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Progress in mathematical physics
Series volume
v. 62
Structured data from the Bibframe namespace is licensed under the Creative Commons Attribution 4.0 International License by University of Missouri Libraries. Additional terms may apply to data associated with third party namespaces.
Processing Feedback ...