Vasile Gradinaru
Seminar für angewandte Mathematik
ETH
Zürich, Switzerland
The time-dependent Schrödinger equation in many space dimensions governs the quantum molecular dynamics. In the context of theoretical semi-classical models in quantum mechanics, there is a family of basis functions that are particularly suitable for the approximation of the highly oscillatory solutions of the quantum molecular dynamics in many dimensions. We use these basis functions in order to construct a time-reversible, fully explicit time-stepping algorithm to approximate the solution of the semi-classical nuclear time-dependent Schrödinger equation. The algorithm is robust in the semi-classical limit and allows the treatment of multi-particle problems by thinning out the basis according to a hyperbolic cross approximation in a moving coordinate frame.