Hardcover ISBN:  9780821836248 
Product Code:  CHEL/350.H 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
eBook ISBN:  9781470430269 
Product Code:  CHEL/350.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Hardcover ISBN:  9780821836248 
eBook: ISBN:  9781470430269 
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 
Hardcover ISBN:  9780821836248 
Product Code:  CHEL/350.H 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
eBook ISBN:  9781470430269 
Product Code:  CHEL/350.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Hardcover ISBN:  9780821836248 
eBook ISBN:  9781470430269 
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 DetailsAMS Chelsea PublishingVolume: 350; 1988; 488 ppMSC: 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 twobody 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 twobody 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.
ReadershipGraduate students and research mathematicians interested in quantum mechanics and Schrödinger operators.

Table of Contents

Chapters

Introduction

Part I. The onecenter point interaction

Chapter I. 1. The onecenter point interaction in three dimensions

Chapter I. 2. Coulomb plus onecenter point interaction in three dimensions

Chapter I. 3. The onecenter $\delta $interaction in one dimension

Chapter I. 4. The onecenter $\delta $’interaction in one dimension

Chapter I. 5. The onecenter 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. Selfadjoint 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. Timedependent 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


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

Chapters

Introduction

Part I. The onecenter point interaction

Chapter I. 1. The onecenter point interaction in three dimensions

Chapter I. 2. Coulomb plus onecenter point interaction in three dimensions

Chapter I. 3. The onecenter $\delta $interaction in one dimension

Chapter I. 4. The onecenter $\delta $’interaction in one dimension

Chapter I. 5. The onecenter 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. Selfadjoint 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. Timedependent 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