Gaussian Wave Packet Dynamics in the Diamagnetic H-Atom

The method of Gaussian wave packet (GWP) propagation introduced by Heller is a popular tool for doing time dependent quantum mechanical calculations in particular in molecular and in nuclear physics. We show that this method is also applicable to atomic systems. We concentrate on the H-atom in a strong magnetic field, where a well-known regularization is used to remove the singularity. The Coulomb potential is transformed to a harmonic potential making GWP especially suitable. All equations of motion are obtained in analytic form. The matrix singularity problem encountered in the equations of motion derived from a time dependent variational principle is overcome by using a singular value decomposition (SVD).