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arXiv · 1206.4519

Factorization method and new potentials from the inverted oscillator

David Bermudez·David J. Fernandez C
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Abstract

In this article we will apply the first- and second-order supersymmetric quantum mechanics to obtain new exactly-solvable real potentials departing from the inverted oscillator potential. This system has some special properties; in particular, only very specific second-order transformations produce non-singular real potentials. It will be shown that these transformations turn out to be the so-called complex ones. Moreover, we will study the factorization method applied to the inverted oscillator and the algebraic structure of the new Hamiltonians.

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David Bermudez, David J. Fernandez C. 2012-06-20. Factorization method and new potentials from the inverted oscillator. https://doi.org/10.1016/j.aop.2013.02.015

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