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The Resource Self-adjoint extensions in quantum mechanics : general theory and applications to Schrödinger and Dirac equations with singular potentials, D.M. Gitman, I.V. Tyutin, B.L. Voronov

Self-adjoint extensions in quantum mechanics : general theory and applications to Schrödinger and Dirac equations with singular potentials, D.M. Gitman, I.V. Tyutin, B.L. Voronov

Creator
Contributor
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
Language
eng
Work
Publication
Extent
1 online resource (xiii, 511 pages).
Contents
  • Dirac Operator with Coulomb Field
  • Schrödinger and Dirac Operators with Aharonov-Bohm and Magnetic-Solenoid Fields
  • Introduction
  • Linear Operators in Hilbert Spaces
  • Basics of the Theory of Self-adjoint Extensions of Symmetric Operators
  • Differential Operators
  • Spectral Analysis of Self-adjoint Operators
  • Free One-Dimensional Particle on an Interval
  • A One-Dimensional Particle in a Potential Field
  • Schrödinger Operators with Exactly Solvable Potentials
Isbn
9786613710925
Instance
Label
Self-adjoint extensions in quantum mechanics : general theory and applications to Schrödinger and Dirac equations with singular potentials
Title
Self-adjoint extensions in quantum mechanics
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
http://library.link/vocab/creatorName
Gitman, D. M
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
http://library.link/vocab/relatedWorkOrContributorName
  • Ti︠u︡tin, I. V.
  • Voronov, B. L.
Series statement
Progress in mathematical physics
Series volume
v. 62
http://library.link/vocab/subjectName
  • Quantum theory
  • Schrödinger equation
  • Dirac equation
  • Mathematical Concepts
  • Mathematics
  • Physics
  • Quantum Theory
  • SCIENCE
  • Dirac equation
  • Quantum theory
  • Schrödinger equation
Label
Self-adjoint extensions in quantum mechanics : general theory and applications to Schrödinger and Dirac equations with singular potentials, D.M. Gitman, I.V. Tyutin, B.L. Voronov
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Dirac Operator with Coulomb Field
  • Schrödinger and Dirac Operators with Aharonov-Bohm and Magnetic-Solenoid Fields
  • Introduction
  • Linear Operators in Hilbert Spaces
  • Basics of the Theory of Self-adjoint Extensions of Symmetric Operators
  • Differential Operators
  • Spectral Analysis of Self-adjoint Operators
  • Free One-Dimensional Particle on an Interval
  • A One-Dimensional Particle in a Potential Field
  • Schrödinger Operators with Exactly Solvable Potentials
Control code
793342284
Dimensions
unknown
Extent
1 online resource (xiii, 511 pages).
File format
unknown
Form of item
online
Isbn
9786613710925
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-0-8176-4662-2
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)793342284
Label
Self-adjoint extensions in quantum mechanics : general theory and applications to Schrödinger and Dirac equations with singular potentials, D.M. Gitman, I.V. Tyutin, B.L. Voronov
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Dirac Operator with Coulomb Field
  • Schrödinger and Dirac Operators with Aharonov-Bohm and Magnetic-Solenoid Fields
  • Introduction
  • Linear Operators in Hilbert Spaces
  • Basics of the Theory of Self-adjoint Extensions of Symmetric Operators
  • Differential Operators
  • Spectral Analysis of Self-adjoint Operators
  • Free One-Dimensional Particle on an Interval
  • A One-Dimensional Particle in a Potential Field
  • Schrödinger Operators with Exactly Solvable Potentials
Control code
793342284
Dimensions
unknown
Extent
1 online resource (xiii, 511 pages).
File format
unknown
Form of item
online
Isbn
9786613710925
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-0-8176-4662-2
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)793342284

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