Distorted Heisenberg Algebra and Coherent States for Isospectral Oscillator Hamiltonians

Abstract

The dynamical algebra associated to a family of isospectral oscillator Hamiltonians is studied through the analysis of its representation in the basis of energy eigenstates. It is shown that this representation becomes similar to that of the standard Heisenberg algebra, and it is dependent of a parameter $w\ge 0$. We name it {\it distorted Heisenberg algebra}, where $w$ is the distortion parameter. The corresponding coherent states for an arbitrary $w$ are derived, and some particular examples are discussed in full detail. A prescription to produce the squeezing, by adequately selecting the initial state of the system, is given.

21 pages, Latex, 3 figures available as hard copies upon request from the first Author

References in corpus (1)

• Geometric Phases and Mielnik's Evolution Loops

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