Peter Winkler
University of Nevada, USA
Title: Siegert’s curse and redemption: Taming and domesticating divergent wave functions
Biography
Biography: Peter Winkler
Abstract
Metastable states of quantum systems can be evaluated as complex-valued eigen solutions of the time-independent Schrődinger equation if complex boundary conditions are applied. Such resonance boundary conditions have been formulated in the early days of quantum mechanics but, initially few calculations have been performed utilizing this concept because the corresponding wave functions diverge asymptotically. Subsequent advances in the computation of energies and widths of metastable states will be discussed when Siegert boundary conditions are applied to achieve the necessary analytic continuation onto the complex energy plane as well as schemes to sidestep the divergences altogether. Examples including potential resonances and multiply excited electronic states of atoms and ions illustrate the wide applicability of this approach.