The -symmetric Rosen-Morse II potential

Effects of the asymptotically non-vanishing imaginary potential component

G. Lévai, E. Magyari

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

Bound and scattering solutions of the -symmetric Rosen-Morse II potential are investigated. The energy eigenvalues and the corresponding wavefunctions are written in a closed analytic form, and it is shown that this potential always supports at least one bound state. It is found that with increasing non-Hermiticity the real bound-state energy spectrum does not turn into complex conjugate pairs, i.e. the spontaneous breakdown of symmetry does not occur, rather the energy eigenvalues remain real and shift to positive values. Closed expression is found for the pseudo-norm of the bound states, and its sign is found to follow the (-1)n rule. Similarly to the known scattering examples, the reflection coefficients exhibit a handedness effect, while the transmission coefficient picks up a complex phase factor when the direction of the incoming wave is reversed. It is argued that the unusual findings might be caused by the asymptotically non-vanishing, though finite imaginary potential component. Comparison with the real Rosen-Morse II potential is also made.

Original languageEnglish
Article number195302
JournalJournal of Physics A: Mathematical and Theoretical
Volume42
Issue number19
DOIs
Publication statusPublished - 2009

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Bound States
Scattering
Wave functions
Electron energy levels
Eigenvalue
Complex conjugate
Closed
eigenvalues
Transmission Coefficient
Reflection Coefficient
Energy Spectrum
Energy
handedness
Breakdown
scattering
norms
Norm
Symmetry
energy spectra
breakdown

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Modelling and Simulation
  • Statistics and Probability

Cite this

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