An adaptive pseudospectral method for wave packet dynamics

Emil Kieri
Division of Scientific Computing
Department of Information Technology
Uppsala University


We solve the time-dependent Schrödinger equation for molecular dynamics using a pseudospectral method with global, exponentially decaying, Hagedorn basis functions. The approximation properties of the Hagedorn basis depend strongly on the scaling of the spatial coordinates. Using results from control theory we develop a time-dependent scaling which adaptively matches the basis to the wave packet. The method requires no knowledge of the Hessian of the potential.