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Solvable Models in Quantum Mechanics: Second Edition
 
S. Albeverio University of Bonn, Bonn, Germany
F. Gesztesy University of Missouri, Columbia, MO
H. Holden Norwegian University of Science & Technology, Trondheim, Norway
Solvable Models in Quantum Mechanics
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-0-8218-3624-8
Product Code:  CHEL/350.H
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $62.10
eBook ISBN:  978-1-4704-3026-9
Product Code:  CHEL/350.H.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Hardcover ISBN:  978-0-8218-3624-8
eBook: ISBN:  978-1-4704-3026-9
Product Code:  CHEL/350.H.B
List Price: $134.00 $101.50
MAA Member Price: $120.60 $91.35
AMS Member Price: $120.60 $91.35
Solvable Models in Quantum Mechanics
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Solvable Models in Quantum Mechanics: Second Edition
S. Albeverio University of Bonn, Bonn, Germany
F. Gesztesy University of Missouri, Columbia, MO
H. Holden Norwegian University of Science & Technology, Trondheim, Norway
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-0-8218-3624-8
Product Code:  CHEL/350.H
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $62.10
eBook ISBN:  978-1-4704-3026-9
Product Code:  CHEL/350.H.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Hardcover ISBN:  978-0-8218-3624-8
eBook ISBN:  978-1-4704-3026-9
Product Code:  CHEL/350.H.B
List Price: $134.00 $101.50
MAA Member Price: $120.60 $91.35
AMS Member Price: $120.60 $91.35
  • Book Details
     
     
    AMS Chelsea Publishing
    Volume: 3501988; 488 pp
    MSC: Primary 81; Secondary 03;

    This monograph presents a detailed study of a class of solvable models in quantum mechanics that describe the motion of a particle in a potential having support at the positions of a discrete (finite or infinite) set of point sources. Both situations–where the strengths of the sources and their locations are precisely known and where these are only known with a given probability distribution–are covered.

    The authors present a systematic mathematical approach to these models and illustrate its connections with previous heuristic derivations and computations. Results obtained by different methods in disparate contexts are thus unified and a systematic control over approximations to the models, in which the point interactions are replaced by more regular ones, is provided.

    The first edition of this book generated considerable interest for those learning advanced mathematical topics in quantum mechanics, especially those connected to the Schrödinger equations. This second edition includes a new appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around two-body point interaction problems, is followed by a bibliography focusing on essential developments made since 1988. appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around two-body point interaction problems, is followed by a bibliography focusing on essential developments made since 1988.

    The material is suitable for graduate students and researchers interested in quantum mechanics and Schrödinger operators.

    Readership

    Graduate students and research mathematicians interested in quantum mechanics and Schrödinger operators.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Part I. The one-center point interaction
    • Chapter I. 1. The one-center point interaction in three dimensions
    • Chapter I. 2. Coulomb plus one-center point interaction in three dimensions
    • Chapter I. 3. The one-center $\delta $-interaction in one dimension
    • Chapter I. 4. The one-center $\delta $’-interaction in one dimension
    • Chapter I. 5. The one-center point interaction in two dimensions
    • Part II. Point interactions with a finite number of centers
    • Chapter II. 1. Finitely many point interactions in three dimensions
    • Chapter II. 2. Finitely many $\delta $-interactions in one dimension
    • Chapter II. 3. Finitely many $\delta $’-interactions in one dimension
    • Chapter II. 4. Finitely many point interactions in two dimensions
    • Part III. Point interactions with infinitely many centers
    • Chapter III. 1. Infinitely many point interactions in three dimensions
    • Chapter III. 2. Infinitely many $\delta $-interactions in one dimension
    • Chapter III. 3. Infinitely many $\delta $’-interactions in one dimension
    • Chapter III. 4. Infinitely many point interactions in two dimensions
    • Chapter III. 5. Random Hamiltonians with point interactions
    • Appendices
    • A. Self-adjoint extensions of symmetric operators
    • B. Spectral properties of Hamiltonians defined as quadratic forms
    • C. Schrödinger operators with interactions concentrated around infinitely many centers
    • D. Boundary conditions for Schrödinger operators on $(0,\infty )$
    • E. Time-dependent scattering theory for point interactions
    • F. Dirichlet forms for point interactions
    • G. Point interactions and scales of Hilbert spaces
    • H. Nonstandard analysis and point interactions
    • I. Elements of probability theory
    • J. Relativistic point interactions in one dimension
  • Reviews
     
     
    • There is a wealth of very pretty examples of Schrödinger operators here which could be presented ... in an elementary quantum mechanics course.

      MathSciNet
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 3501988; 488 pp
MSC: Primary 81; Secondary 03;

This monograph presents a detailed study of a class of solvable models in quantum mechanics that describe the motion of a particle in a potential having support at the positions of a discrete (finite or infinite) set of point sources. Both situations–where the strengths of the sources and their locations are precisely known and where these are only known with a given probability distribution–are covered.

The authors present a systematic mathematical approach to these models and illustrate its connections with previous heuristic derivations and computations. Results obtained by different methods in disparate contexts are thus unified and a systematic control over approximations to the models, in which the point interactions are replaced by more regular ones, is provided.

The first edition of this book generated considerable interest for those learning advanced mathematical topics in quantum mechanics, especially those connected to the Schrödinger equations. This second edition includes a new appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around two-body point interaction problems, is followed by a bibliography focusing on essential developments made since 1988. appendix by Pavel Exner, who has prepared a summary of the progress made in the field since 1988. His summary, centering around two-body point interaction problems, is followed by a bibliography focusing on essential developments made since 1988.

The material is suitable for graduate students and researchers interested in quantum mechanics and Schrödinger operators.

Readership

Graduate students and research mathematicians interested in quantum mechanics and Schrödinger operators.

  • Chapters
  • Introduction
  • Part I. The one-center point interaction
  • Chapter I. 1. The one-center point interaction in three dimensions
  • Chapter I. 2. Coulomb plus one-center point interaction in three dimensions
  • Chapter I. 3. The one-center $\delta $-interaction in one dimension
  • Chapter I. 4. The one-center $\delta $’-interaction in one dimension
  • Chapter I. 5. The one-center point interaction in two dimensions
  • Part II. Point interactions with a finite number of centers
  • Chapter II. 1. Finitely many point interactions in three dimensions
  • Chapter II. 2. Finitely many $\delta $-interactions in one dimension
  • Chapter II. 3. Finitely many $\delta $’-interactions in one dimension
  • Chapter II. 4. Finitely many point interactions in two dimensions
  • Part III. Point interactions with infinitely many centers
  • Chapter III. 1. Infinitely many point interactions in three dimensions
  • Chapter III. 2. Infinitely many $\delta $-interactions in one dimension
  • Chapter III. 3. Infinitely many $\delta $’-interactions in one dimension
  • Chapter III. 4. Infinitely many point interactions in two dimensions
  • Chapter III. 5. Random Hamiltonians with point interactions
  • Appendices
  • A. Self-adjoint extensions of symmetric operators
  • B. Spectral properties of Hamiltonians defined as quadratic forms
  • C. Schrödinger operators with interactions concentrated around infinitely many centers
  • D. Boundary conditions for Schrödinger operators on $(0,\infty )$
  • E. Time-dependent scattering theory for point interactions
  • F. Dirichlet forms for point interactions
  • G. Point interactions and scales of Hilbert spaces
  • H. Nonstandard analysis and point interactions
  • I. Elements of probability theory
  • J. Relativistic point interactions in one dimension
  • There is a wealth of very pretty examples of Schrödinger operators here which could be presented ... in an elementary quantum mechanics course.

    MathSciNet
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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