HILBERT SPACE METHODS IN QUANTUM MECHANICS

This book provides the necessary foundation in quantum mechanics. Specific topics include basic properties of Hilbert spaces; bounded linear operators with general notions of unbounded operators; self-adjointness, including the theory of extensions of symmetric operators with applications to Sturm-Liouville and Schrödinger operators; spectral theory of self-adjoint operators; Stone's theorem; scattering theory, including stationary-state scattering theory; the Moure method; and a number of applications, such as the S-matrix, time delay and the Flux-Across-Surfaces Theorem.