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Journal of Mathematical Physics

Parametric-time coherent states for Smorodinsky-Winternitz potentials

Nuri Ünal

Published Dec 1, 2007• 7 citations
Publisher

Abstract

In this study, we construct the coherent states for a particle in the Smorodinsky-Winternitz potentials, which are the generalizations of the two-dimensional Kepler problem. In the third case, the system is transformed into four ocillators and the parametric-time coherent states are constructed in two coordinate frames. In the fourth case, the system is transformed into two ocillators with the reflection symmetry and the parametric-time coherent states are constructed in two coordinate frames.

DOI
10.1063/1.2824498

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In this study, we construct the coherent states for a particle in the Smorodinsky-Winternitz potentials, which are the generalizations of the two-dimensional Kepler problem. In the third case, the system is transformed into four ocillators and the parametric-time coherent states are constructed in two coordinate frames. In the fourth case, the system is transformed into two ocillators with the reflection symmetry and the parametric-time coherent states are constructed in two coordinate frames.
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Abstract In this study, we construct the coherent states for a particle in the Smorodinsky-Winternitz potentials, which are the generalizations of the two-dimensional harmonic oscillator problem. In the first case, we find the non-spreading wave packets by transforming the system into four oscillators in Cartesian, and also polar, coordinates. In the second case, the coherent states are constructed in Cartesian coordinates by transforming the system into three non-isotropic harmonic oscillators. All of these states evolve in physical-time. We also show that in parametric-time, the second case can be transformed to the first one with vanishing eigenvalues.