Numerical methods in quantum dynamics

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The project deals with numerical methods for molecular quantum dynamics, both in devising new methods and in the mathematical analysis of known and novel methods. The numerical difficulties lie in the high dimensionality of the underlying Schrödinger equation as the basic model equation as wellas in the treatment of high oscillations and multiple scales. The project focuses on time-dependent aspects, complementing approaches to the stationary Schrödinger eigenvalue problem within the Priority Research Programme. The research will concentrate on dynamical low-rank approximations such as the time-dependent multi-configuration Hartree and Hartree-Fock methods on the one hand, and on a novel computational approach to the time-dependent Schrödinger equation in semi-classical scaling (for nuclei in a molecule) based on Hagedorn wavepackets.