Schrödinger Operators: With Applications to Quantum Mechanics and Global GeometryA 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. |
Contents
SelfAdjointness | 1 |
LPProperties of Eigenfunctions and All That | 13 |
Geometric Methods for Bound States | 27 |
Local Commutator Estimates | 60 |
1 | 71 |
17 | 107 |
1 | 115 |
Notes Added for this Reprint | 134 |
Formula | 186 |
24 | 187 |
Almost Periodic Jacobi Matrices | 203 |
Notes Added for this Reprint | 223 |
Wittens Proof of the Morse Inequalities | 224 |
Patodis Proof of the GaussBonnetChern Theorem and Superproofs | 245 |
Bibliography | 307 |
References Added for this Reprint | 321 |