2010, Vol.13, No.1, pp.38-44
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 states also in these systems. This is achieved
by a regularization of the Coulomb potential, and by introduction of a
fictitious time coordinate in which the evolution of an initial state can
be calculated exactly and analytically for a pure Coulomb potential.
Therefore in perturbed atomic systems variational approximations only arise
from those parts of the potentials which deviate from the Coulomb potential.
The method is applied to the hydrogen atom in external magnetic
and electric fields. It can be adapted to systems with definite symmetries,
and thus allows for a wide range of applications.
Key words: hydrogen atom in external magnetic and electric fields, Coulomb potential, Gaussian wave packets
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