New supersymmetry-generated complex potentials with real spectra

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 Schrödinger type. The superpotentials so constructed...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 48; no. 44; pp. 445302 - 23
Main Authors Rosas-Ortiz, Oscar, Castaños, Octavio, Schuch, Dieter
Format Journal Article
LanguageEnglish
Published IOP Publishing 06.11.2015
Subjects
complex potentials with real spectra
Construction
Differential equations
Eigenvalues
free particle
harmonic oscillator
Mathematical analysis
Oscillators
Pöschl-Teller potential
Schroedinger equation
Spectra
supersymmetric quantum mechanics
Supersymmetry
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Summary: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 Schrödinger 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 -symmetric and can be either periodic or regular (of the Pöschl-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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ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/48/44/445302