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

TL;DR

This paper extends the fictitious time wave packet method to the hydrogen atom in external fields, enabling accurate and efficient quantum dynamics simulations using a variational approach with Gaussian wave packets.

Contribution

It develops a Gaussian wave packet method for hydrogen in external fields using the time-dependent variational principle, incorporating couplings due to external fields and enabling eigenvalue computation.

Findings

Exact propagation for field-free hydrogen in fictitious time.

Numerical propagation of coupled wave packets in external fields.

Eigenvalues obtained via frequency analysis of autocorrelation functions.

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.