Asymptotic observables for quantum Hamiltonians with external fields

Abstract

The description of the large-time asymptotic behaviour of scattering states via selected time-dependent observables has proven tremendously important in quantum mechanical scattering, in particular for establishing asymptotic completeness. The thesis presents new results for such asymptotic observables for a class of quantum Hamiltonians with external fields. The first part of the thesis presents the necessary mathematical theory and methods used to establish the results including an introduction to scattering theory (physics level), elements of linear operator theory, elements of mathematical scattering theory (decomposition of the spectrum and characterisation of scattering states, the Møller wave operators etc), and a classic result on asymptotic completeness. The second part presents the new results with detailed proofs.