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




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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/



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