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Factorization method and new potentials from the inverted oscillator
Authors:David Bermudez,David J. Ferná  ndez C.
Affiliation:Departamento de Física, Cinvestav, A.P. 14-740, 07000 México D.F., Mexico
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.
Keywords:Supersymmetric quantum mechanics   Darboux transformations   Harmonic oscillator   Inverted oscillator
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