**Proceedings of Symposia in Pure Mathematics**

Volume: 76;
2007;
496 pp;
Hardcover

MSC: Primary 35; 47; 81; 82;

Print ISBN: 978-0-8218-4248-5

Product Code: PSPUM/76.1

List Price: $120.00

Individual Member Price: $96.00

**Electronic ISBN: 978-0-8218-9382-1
Product Code: PSPUM/76.1.E**

List Price: $120.00

Individual Member Price: $96.00

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# Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon’s 60th Birthday: Quantum Field Theory, Statistical Mechanics, and Nonrelativistic Quantum Systems

Share this page *Edited by *
*Fritz Gesztesy; Percy Deift; Cherie Galvez; Peter Perry; Wilhelm Schlag*

This Festschrift had its origins in a conference called SimonFest held
at Caltech, March 27–31, 2006, to honor Barry Simon's 60th
birthday. It is not a proceedings volume in the usual sense since the
emphasis of the majority of the contributions is on reviews of the
state of the art of certain fields, with particular focus on recent
developments and open problems. The bulk of the articles in this
Festschrift are of this survey form, and a few review Simon's
contributions to a particular area. Part 1 contains surveys in the
areas of Quantum Field Theory, Statistical Mechanics, Nonrelativistic
Two-Body and \(N\)-Body Quantum Systems, Resonances, Quantum
Mechanics with Electric and Magnetic Fields, and the Semiclassical
Limit. Part 2 contains surveys in the areas of Random and Ergodic
Schrödinger Operators, Singular Continuous Spectrum, Orthogonal
Polynomials, and Inverse Spectral Theory. In several cases, this
collection of surveys portrays both the history of a subject and its
current state of the art. Exhaustive lists of references enhance the
presentation offered in these surveys.

A substantial part of the contributions to this Festschrift are
survey articles on the state of the art of certain areas with special
emphasis on open problems. This will benefit graduate students as well as
researchers who want to get a quick, yet comprehensive introduction into an
area covered in this volume.

#### Table of Contents

# Table of Contents

## Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday: Quantum Field Theory, Statistical Mechanics, and Nonrelativistic Quantum Systems

- Contents v6
- Part 1. Quantum Field Theory, Statistical Mechanics, and Nonrelativistic Quantum Systems iii4 free
- Preface ix10 free
- A Mathematical Genealogy xiii14 free
- A Selection of Barry Stories xvii18 free
- Quantum Field Theory, Statistical Mechanics 128 free
- Nonrelativistic Two-Body and N-Body Quantum Systems, Resonances 103130
- Isoperimetric Inequalities for Eigenvalues of the Laplacian 105132
- Non-Self-Adjoint Operators and Pseudospectra 141168
- Barry Simon's Contributions to Non-Relativistic Quantum Mechanics: Two-Body and N-Body Schrödinger Operators and Resonances 153180
- N-Body Quantum Scattering and Quantum Resonances: An Overview 169196
- Mathematical Analysis of Born–Oppenheimer Approximations 203230
- Perturbation Theory and Atomic Resonances Since Schrödinger's Time 227254
- On a Theorem for Quantum Mechanical Scattering Theory 249276
- Analytic Criteria in the Qualitative Spectral Analysis of the Schrödinger Operator 257284
- The Spectral Geometry of Geometrically Finite Hyperbolic Manifolds 289316
- Topics in the Theory of Positive Solutions of Second-Order Elliptic and Parabolic Partial Differential Equations 329356
- Complex Scaling in Atomic Physics: A Staging Ground for Experimental Mathematics and for Extracting Physics from Otherwise Impossible Computations 357384
- Recent Results on the Bethe–Sommerfeld Conjecture 383410

- Electric and Magnetic Fields, Semiclassical Limit 399426

#### Readership

Research mathematicians interested in mathematical physics and spectral theory.