On the pseudo-norm and admissible solutions of the PT-symmetric Scarf I potential

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The physically admissible solutions of the -symmetric Scarf I potential are identified in the domain of real and complex energies. It is found that generally there are no admissible complex-energy solutions, and there is one with real energy. In a limited range of the parameters there are two series of seemingly admissible solutions both with the real and complex energies belonging to quasi-parity q ≤ ±; however, the two sets are not -orthogonal in the domain of real energies. The sign of the pseudo-norm of states with real energy is found to oscillate as (-1)n, in accordance with the example of other -symmetric potentials possessing an infinite number of discrete levels. It is argued that the spontaneous breakdown of -symmetry cannot be defined for the Scarf I potential. A comparison with some -symmetric extensions of the infinite square well is presented.

Original languageEnglish
Article numberS17
Pages (from-to)10161-10169
Number of pages9
JournalJournal of Physics A: Mathematical and General
Issue number32
Publication statusPublished - Aug 11 2006


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

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