Comparative analysis of real and PT-symmetric Scarf potentials

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The Scarf I and Scarf II potentials are discussed within a common mathematical framework, which is then specified to handle the two potentials separately both in the conventional Hermitian and in the PT-symmetric setting. The physically admissible solutions are identified in each case together with the corresponding energy eigenvalues. Several main differences between the PT-symmetric Scarf I and II potentials are pointed out. These include the presence and absence of the quasi-parity quantum number, the sign of the pseudo-norm, the mechanism of the spontaneous breakdown of PT symmetry and the non- PT orthogonality of otherwise admissible solutions in the Scarf I potential. Similarities and differences with respect to the corresponding Hermitian systems are also pointed out.

Original languageEnglish
Pages (from-to)953-966
Number of pages14
JournalCzechoslovak Journal of Physics
Issue number9
Publication statusPublished - Sep 1 2006


  • PT symmetry
  • Pseudo-norm
  • Singular potentials
  • Spontaneous breakdown of PT symmetry

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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