Schrödinger Operators: With Applications to Quantum Mechanics and Global Geometry

ISBN-13: 9783540167587 / Angielski / Miękka / 1987 / 329 str.

Richard G. Froese; Werner Kirsch; Barry Simon

Opis

Are you looking for a concise summary of the theory of Schrodinger operators? Here it is. Emphasizing the progress made in the last decade by Lieb, Enss, Witten and others, the three authors don t just cover general properties, but also detail multiparticle quantum mechanics including bound states of Coulomb systems and scattering theory. This corrected and extended reprint contains updated references as well as notes on the development in the field over the past twenty years."

Spis treści

Self-Adjointness.- Lp-Properties of Eigenfunctions, and All That.- Geometric Methods for Bound States.- Local Commutator Estimates.- Phase Space Analysis of Scattering.- Magnetic Fields.- Electric Fields.- Complex Scaling.- Random Jacobi Matrices.- Almost Periodic Jacobi Matrices.- Witten's Proof of the Morse Inequalities.- Patodi's Proof of the Gauss-Bonnet-Chern Theorem and Superproofs of Index Theorems.- Bibliography.- List of Symbols.- Subject Index.

O autorze

Dipl.-Ing. Werner Kirsch arbeitet als selbstständiger Bauingenieur und unterhält ein eigenes Ingenieurbüro für Tragwerksplanung.

Blurb

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.