期刊
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
卷 48, 期 44, 页码 -出版社
IOP Publishing Ltd
DOI: 10.1088/1751-8113/48/44/445302
关键词
supersymmetric quantum mechanics; complex potentials with real spectra; Poschl-Teller potential; harmonic oscillator; free particle
资金
- CONACyT [238494, 152574]
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 Schrodinger 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 Poschl-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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