**Mathematical Surveys and Monographs**

Volume: 90;
2002;
242 pp;
Hardcover

MSC: Primary 35; 34; 47; 81;

Print ISBN: 978-0-8218-2919-6

Product Code: SURV/90

List Price: $78.00

AMS Member Price: $62.40

MAA member Price: $70.20

**Electronic ISBN: 978-1-4704-1317-0
Product Code: SURV/90.E**

List Price: $78.00

AMS Member Price: $62.40

MAA member Price: $70.20

# Multiparticle Quantum Scattering in Constant Magnetic Fields

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*Christian Gérard; Izabella Łaba*

This monograph offers a rigorous mathematical treatment of the scattering
theory of quantum N-particle systems in an external constant magnetic field. In
particular, it addresses the question of asymptotic completeness, a
classification of all possible trajectories of such systems according to their
asymptotic behavior. The book adopts the so-called time-dependent approach to
scattering theory, which relies on a direct study of the Schrödinger
unitary group for large times. The modern methods of spectral and scattering
theory introduced in the 1980s and 1990s, including the Mourre theory of
positive commutators, propagation estimates, and geometrical techniques, are
presented and heavily used. Additionally, new methods were developed by the
authors in order to deal with the (much less understood) phenomena due to the
presence of the magnetic field.

The book is a good starting point for graduate students and researchers in
mathematical physics who wish to move into this area of research. It includes
expository material, research work previously available only in the form of
journal articles, as well as some new unpublished results. The treatment of the
subject is comprehensive and largely self-contained, and the text is carefully
written with attention to detail.

#### Readership

Graduate students and research mathematicians interested in mathematical physics and differential equations.

#### Reviews & Endorsements

The book is well organized and well written … the authors have successfully achieved their stated aim of writing a book which is of interest both to a wider section of the mathematical physics community … and to graduate students and researchers in the field of spectral and scattering theory for magnetic Schrödinger operators.

-- Mathematical Reviews

#### Table of Contents

# Table of Contents

## Multiparticle Quantum Scattering in Constant Magnetic Fields

- Contents vii8 free
- Preface ix10 free
- Notation xi12 free
- Chapter 1. Fundamentals 116 free
- Chapter 2. Geometrical Methods I 4560
- Chapter 3. The Mourre Theory 6580
- 3.1. Local inequalities for operators 6883
- 3.2. Basics of the Mourre theory 7186
- 3.3. The strongly charged case 7489
- 3.4. Analytically fibered operators 8095
- 3.5. Two-particle neutral systems 8499
- 3.6. Dispersive channels 94109
- 3.7. Three-dimensional dispersive systems 104119
- 3.8. Two-dimensional dispersive systems 141156

- Chapter 4. Basic Propagation Estimates 143158
- Chapter 5. Geometrical Methods II 167182
- Chapter 6. Wave Operators and Scattering Theory 201216
- Chapter 7. Open Problems 227242
- Chapter 8. Appendix 231246
- Bibliography 235250
- Index 241256