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arXiv · 1505.05197

New supersymmetry-generated complex potentials with real spectra

Oscar Rosas-Ortiz·Octavio Castanos·Dieter Schuch
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Abstract

A new form to construct complex superpotentials that produce real energy spectra in supersymmetric quantum mechanics is presented. This is based on the relation between the nonlinear Ermakov equation and a second order differential equation of the Schroedinger type. The superpotentials so constructed are characterized by the Ermakov parameters in such a way that they are always complex-valued and lead to non-Hermitian Hamiltonians with real spectra, whose eigenfunctions form a bi-orthogonal system. As applications we present new complex supersymmetric partners of the free particle that are PT-symmetric and can be either periodic or regular (of the Poeschl-Teller form). A new family of complex oscillators with real frequencies that have the energies of the harmonic oscillator plus an additional real eigenvalue is introduced.

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Oscar Rosas-Ortiz, Octavio Castanos, Dieter Schuch. 2015-05-19. New supersymmetry-generated complex potentials with real spectra. https://doi.org/10.1088/1751-8113%2F48%2F44%2F445302

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