Algebraic and scattering aspects of a PT-symmetric solvable potential

G. Lévai, F. Cannata, A. Ventura

Research output: Contribution to journalArticle

70 Citations (Scopus)

Abstract

We study a particular solvable potential and analyse the effect of PT symmetry on its bound state as well as scattering solutions. We determine the transmission and reflection coefficients for the PT-symmetric case and also formulate the problem in terms of an SU (1, 1) potential group, which allows unified treatment of the discrete and the continuous spectra in a natural way. We find that (bound and scattering) states of the PT-symmetric problem supply a basis for the unitary irreducible representations of the SU (1, 1) potential group, and this gives a straightforward group theoretical interpretation of the fact that the (complex) PT-invariant potential has a real energy spectrum.

Original languageEnglish
Pages (from-to)839-844
Number of pages6
JournalJournal of Physics A: Mathematical and General
Volume34
Issue number4
DOIs
Publication statusPublished - Feb 2 2001

ASJC Scopus subject areas

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

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