Rauh, Alexander (2016) Coherent States of Harmonic and Reversed Harmonic Oscillator. Symmetry, 8(6) (46). ISSN 2073-8994

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A one-dimensional wave function is assumed whose logarithm is a quadratic form in the configuration variable with time-dependent coefficients. This trial function allows for general time-dependent solutions both of the harmonic oscillator (HO) and the reversed harmonic oscillator (RO). For the HO, apart from the standard coherent states, a further class of solutions is derived with a time-dependent width parameter. The width of the corresponding probability density fluctuates, or "breathes" periodically with the oscillator frequency. In the case of the RO, one also obtains normalized wave packets which, however, show diffusion through exponential broadening with time. At the initial time, the integration constants give rise to complete sets of coherent states in the three cases considered. The results are applicable to the quantum mechanics of the Kepler-Coulomb problem when transformed to the model of a four-dimensional harmonic oscillator with a constraint. In the classical limit, as was shown recently, the wave packets of the RO basis generate the hyperbolic Kepler orbits, and, by means of analytic continuation, the elliptic orbits are also obtained quantum mechanically.

Item Type: Article
Additional Information: Publiziert mit Hilfe des DFG-geförderten Open Access-Publikationsfonds der Carl von Ossietzky Universität Oldenburg.
Uncontrolled Keywords: inverted harmonic oscillator; harmonic trap; Kepler-Coulomb problem; Kustaanheimo-Stiefel transformation
Subjects: Science and mathematics > Physics
Divisions: Faculty of Mathematics and Science > Institute of Physics (IfP)
Date Deposited: 17 Jan 2017 11:06
Last Modified: 23 Jun 2017 12:51
URI: https://oops.uni-oldenburg.de/id/eprint/2930
URN: urn:nbn:de:gbv:715-oops-30111
DOI: 10.3390/sym8060046

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