Fictitious-time wave-packet dynamics. II. Hydrogen atom in external fields

In the preceding paper [ T. Fabčič, J. Main and G. Wunner Phys. Rev. A 79 043416 (2009)] “restricted Gaussian wave packets” were introduced for the regularized Coulomb problem in the four-dimensional Kustaanheimo-Stiefel coordinates, and their exact time propagation was derived analytically in a fictitious-time variable. We now establish the Gaussian wave-packet method for the hydrogen atom in static external fields. A superposition of restricted Gaussian wave packets is used as a trial function in the application of the time-dependent variational principle. The external fields introduce couplings between the basis states. The set of coupled wave packets is propagated numerically, and eigenvalues of the Schrödinger equation are obtained by the frequency analysis of the time autocorrelation function. The advantage of the wave-packet propagation in the fictitious-time variable is that the computations are exact for the field-free hydrogen atom and approximations from the time-dependent variational principle only stem from the external fields. Examples are presented for the hydrogen atom in a magnetic field and in crossed electric and magnetic fields.