1206.4519 (David Bermudez et al.)

New exactly-solvable potentials from inverted oscillator    [PDF]

David Bermudez, David J. Fernandez C

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 properties which make it special, 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.

View original: http://arxiv.org/abs/1206.4519