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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Published in | Journal of physics. A, Mathematical and theoretical Vol. 48; no. 44; pp. 445302 - 23 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
IOP Publishing
06.11.2015
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Subjects | |
Online Access | Get full text |
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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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Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
ISSN: | 1751-8113 1751-8121 |
DOI: | 10.1088/1751-8113/48/44/445302 |