Factorization method and new potentials from the inverted oscillator

Understand

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.