Fictitious-Time Wave-Packet Dynamics in Atomic Systems

Fictitious-Time Wave-Packet Dynamics in Atomic Systems

Gaussian wave packets (GWPs) are well suited as basis functions to describe the time evolution of arbitrary wave functions in systems with non-singular smooth potentials. They are rare in atomic systems on account of the singular behaviour of the Coulomb potential. We present a time-dependent variational method that makes the use of GWPs possible in the description of propagation of quantum sta...

2 7 M ay 2 00 9 Fictitious - time wave - packet dynamics in atomic systems

Gaussian wave packets (GWPs) are well suited as basis functions to describe the time evolution of arbitrary wave functions in systems with nonsingular smooth potentials. They are less so in atomic systems on account of the singular behavior of the Coulomb potential. We present a time-dependent variational method that makes the use of GWPs possible in the description of propagation of quantum st...

Fictitious-time wave-packet dynamics. I. Nondispersive wave packets in the quantum Coulomb problem

Nondispersive wave packets in a fictitious time variable are calculated analytically for the field-free hydrogen atom. As is well known by means of the Kustaanheimo-Stiefel transformation the Coulomb problem can be converted into that of a four-dimensional harmonic oscillator, subject to a constraint. This regularization makes use of a fictitious time variable, but arbitrary Gaussian wave packe...

Wave packet dynamics in atomic systems and Bose - Einstein condensates

Fictitious time wave packet dynamics: The hydrogen atom in external fields

In the preceding paper [T. Fabčič 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 superpositi...