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

Abstract

In the preceding paper [T. Fabcic et al., preprint] "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 Schrodinger 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.

13 pages, 6 figures

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Cited by in corpus (5)

• Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. I. General concept
• Variational calculations for anisotropic solitons in dipolar Bose-Einstein condensates
• Pitchfork bifurcations in blood-cell shaped dipolar Bose-Einstein condensates
• Simulation of a Hydrogen Atom in Laser Field Using the Time-Dependent Variational Principle
• Fictitious time wave packet dynamics: I. Nondispersive wave packets in the quantum Coulomb problem