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
Resource Information
The item 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 represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item 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 represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
- 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
- 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
- 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
- Subject
-
- Dirac equation
- Dirac equation
- Dirac equation
- Mathematical Concepts
- Mathematical Methods in Physics.
- Mathematical physics.
- Mathematics
- Mathematics.
- Operator theory.
- Physics
- Quantum Physics.
- Quantum Theory
- Quantum theory -- Mathematics
- Quantum theory -- Mathematics
- Quantum theory -- Mathematics
- Quantum theory.
- SCIENCE -- Physics | Quantum Theory
- Schrödinger equation
- Schrödinger equation
- Schrödinger equation
- Applications of Mathematics.
- 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
- 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
- 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
- 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
Subject
- Dirac equation
- Dirac equation
- Dirac equation
- Mathematical Concepts
- Mathematical Methods in Physics.
- Mathematical physics.
- Mathematics
- Mathematics.
- Operator theory.
- Physics
- Quantum Physics.
- Quantum Theory
- Quantum theory -- Mathematics
- Quantum theory -- Mathematics
- Quantum theory -- Mathematics
- Quantum theory.
- SCIENCE -- Physics | Quantum Theory
- Schrödinger equation
- Schrödinger equation
- Schrödinger equation
- Applications of Mathematics.
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