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Helvetica Physica Acta (Switzerland)

Non-spreading coherent states riding on Kepler orbits

A. O. Barut, Xu Bo-wei

Published Jan 17, 1994• 6 citations
Publisher

Abstract

We construct exact non-spreading coherent states for the Kepler problem and show that they must be two-dimensional lying on the plane of the orbit. The use of a new time variable in the associated auxiliary oscillator problem plays a crucial role
DOI
10.5169/seals-116586

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The Kustaanheino-Stiefel transformation is used to transform the Coulomb problem to a four-dimensional isotropic harmonic oscillator with a constraint. Ordinary coherent states are introduced over this oscillator and are shown to evolve in a fictitious time. When projected back into the physical space, the states follow the classical Kepler orbits in physical time. The resulting quasiclassical picture is obtained without the Bohr correspondence principle of taking only contributions from high principal quantum numbers.
The coherent states for the quantum Kepler motion proposed in our previous work [Phys. Rev. A 59, 1021 (1999)], which is based on the dynamical $\mathrm{SU}(2)\ensuremath{\bigotimes}\mathrm{SU}(2)$ symmetry and the Duru-Kleinert auxiliary time, are improved by making use of the theory of the conserved-charge coherent states formulated by Bhaumik et al. and by Skagertsam. The expectation values for the angular momentum and the Runge-Lenz-Pauli vector with respect to the improved Kepler coherent states are also discussed.