Schrödinger Operators: With Application to Quantum Mechanics and Global Geometry

A complete understanding of SchrAdinger operators is a necessary prerequisite for unveiling the physics of nonrelativistic quanturn 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 SchrAdinger 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, SchrAdinger operators with random and almost periodic potentials and, finally, SchrAdinger operator methods in differential geometry to prove the Morse inequalities and the index theorem.