# Fictitious time wave packet dynamics: I. Nondispersive wave packets in the quantum Coulomb problem - Physics > Atomic Physics

Fictitious time wave packet dynamics: I. Nondispersive wave packets in the quantum Coulomb problem - Physics > Atomic Physics - Download this document for free, or read online. Document in PDF available to download.

Abstract: Nondispersive wave packets in a fictitious time variable are calculatedanalytically for the field-free hydrogen atom.

As is well known by means of theKustaanheimo-Stiefel transformation the Coulomb problem can be converted intothat of a four-dimensional harmonic oscillator, subject to a constraint.

Thisregularization makes use of a fictitious time variable, but arbitrary Gaussianwave packets in that time variable in general violate that constraint.

The setof -restricted Gaussian wave packets- consistent with the constraint isconstructed and shown to provide a complete basis for the expansion of statesin the original three-dimensional coordinate space.

Using that expansionarbitrary localized Gaussian wave packets of the hydrogen atom can bepropagated analytically, and exhibit a nondispersive periodic behavior asfunctions of the fictitious time.

Restricted wave packets with and without welldefined angular momentum quantum n umbers are constructed.

They will be used astrial functions in time-dependent variational computations for the hydrogenatom in static external fields in the subsequent paper T.

Fab\v{c}i\v{c} etal., submitted.

Author: ** T.Fabčič, J.Main, G.Wunner**

Source: https://arxiv.org/