Schrödinger Operators: With Applications to Quantum Mechanics and Global Geometry

✍ Scribed by Hans L. Cycon, Richard G. Froese, Werner Kirsch, Barry Simon, Hans L. Cycon (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1987
• Tongue: English
• Leaves: 337
• Series: Theoretical,Mathematical Physics
• Edition: 1
• Category: Library

✦ Synopsis

A complete understanding of Schrödinger operators is a necessary prerequisite for unveiling the physics of nonrelativistic quantum mechanics. Furthermore recent research shows that it also helps to deepen our insight into global differential geometry. This monograph written for both graduate students and researchers summarizes and synthesizes the theory of Schrödinger operators emphasizing the progress made in the last decade by Lieb, Enss, Witten and others. Besides general properties, the book covers, in particular, multiparticle quantum mechanics including bound states of Coulomb systems and scattering theory, quantum mechanics in constant electric and magnetic fields, Schrödinger operators with random and almost periodic potentials and, finally, Schrödinger operator methods in differential geometry to prove the Morse inequalities and the index theorem.

This corrected and extended reprint contains updated proofs and references as well as notes on the development in the field over the past twenty years.

✦ Table of Contents

Front Matter....Pages I-XI
Self-Adjointness....Pages 1-12
L p -Properties of Eigenfunctions, and All That....Pages 13-26
Geometric Methods for Bound States....Pages 27-59
Local Commutator Estimates....Pages 60-88
Phase Space Analysis of Scattering....Pages 89-114
Magnetic Fields....Pages 115-134
Electric Fields....Pages 135-152
Complex Scaling....Pages 153-167
Random Jacobi Matrices....Pages 168-202
Almost Periodic Jacobi Matrices....Pages 203-223
Witten’s Proof of the Morse Inequalities....Pages 224-244
Patodi’s Proof of the Gauss-Bonnet-Chern Theorem and Superproofs of Index Theorems....Pages 245-306
Back Matter....Pages 307-329

✦ Subjects

Quantum Physics; Quantum Computing, Information and Physics