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DOE OSTI · 22220737

Factorization method and new potentials from the inverted oscillator

Bermudez, David
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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. -- Highlights: •We apply supersymmetric quantum mechanics to the inverted oscillator potential. •The complex second-order transformations allow us to build new non-singular potentials. •The algebraic structure of the initial and final potentials is analyzed. •The initial potential is described by a complex-deformed Heisenberg–Weyl algebra. •The final potentials are described by polynomial Heisenberg algebras.

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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICSEXACT SOLUTIONSFACTORIZATIONHAMILTONIANSHARMONIC OSCILLATORSOSCILLATORSPOLYNOMIALSPOTENTIALSQUANTUM MECHANICSSUPERSYMMETRYTRANSFORMATIONS

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Bermudez, David. 2013-06-15. Factorization method and new potentials from the inverted oscillator. https://doi.org/10.1016/j.aop.2013.02.015

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