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arxiv: 1206.4519 · v3 · pith:QKF5RXCQnew · submitted 2012-06-20 · 🪐 quant-ph · math-ph· math.MP

Factorization method and new potentials from the inverted oscillator

classification 🪐 quant-ph math-phmath.MP
keywords invertedoscillatorpotentialswillfactorizationmethodrealsecond-order
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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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