The Resource Selfadjoint 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
Selfadjoint 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
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The item Selfadjoint 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 Selfadjoint 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 quantummechanical observables, such as the Hamiltonian, momentum, etc., as selfadjoint operators in appropriate Hilbert spaces and their spectral analysis. Though a?naïve? treatment exists for dealing with such problems, it is based on finitedimensional algebra or even infinitedimensional 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 selfadjoint operators and the theory of selfadjoint extensions of symmetric operators. Selfadjoint 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 selfadjoint extensions. Through examination of various quantummechanical 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 quantummechanical systems. Systems that are examined include free particles on an interval, particles in a number of potential fields including deltalike potentials, the onedimensional Calogero problem, the AharonovBohm problem, and the relativistic Coulomb problem. This wellorganized 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 AharonovBohm and MagneticSolenoid Fields
 Introduction
 Linear Operators in Hilbert Spaces
 Basics of the Theory of Selfadjoint Extensions of Symmetric Operators
 Differential Operators
 Spectral Analysis of Selfadjoint Operators
 Free OneDimensional Particle on an Interval
 A OneDimensional Particle in a Potential Field
 Schrödinger Operators with Exactly Solvable Potentials
 Isbn
 9780817646622
 Label
 Selfadjoint extensions in quantum mechanics : general theory and applications to Schrödinger and Dirac equations with singular potentials
 Title
 Selfadjoint 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 quantummechanical observables, such as the Hamiltonian, momentum, etc., as selfadjoint operators in appropriate Hilbert spaces and their spectral analysis. Though a?naïve? treatment exists for dealing with such problems, it is based on finitedimensional algebra or even infinitedimensional 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 selfadjoint operators and the theory of selfadjoint extensions of symmetric operators. Selfadjoint 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 selfadjoint extensions. Through examination of various quantummechanical 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 quantummechanical systems. Systems that are examined include free particles on an interval, particles in a number of potential fields including deltalike potentials, the onedimensional Calogero problem, the AharonovBohm problem, and the relativistic Coulomb problem. This wellorganized 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
 Selfadjoint 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 AharonovBohm and MagneticSolenoid Fields
 Introduction
 Linear Operators in Hilbert Spaces
 Basics of the Theory of Selfadjoint Extensions of Symmetric Operators
 Differential Operators
 Spectral Analysis of Selfadjoint Operators
 Free OneDimensional Particle on an Interval
 A OneDimensional 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
 9780817646622
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9780817646622
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)793342284
 Label
 Selfadjoint 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 AharonovBohm and MagneticSolenoid Fields
 Introduction
 Linear Operators in Hilbert Spaces
 Basics of the Theory of Selfadjoint Extensions of Symmetric Operators
 Differential Operators
 Spectral Analysis of Selfadjoint Operators
 Free OneDimensional Particle on an Interval
 A OneDimensional 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
 9780817646622
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9780817646622
 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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