The interplay of supersymmetry and PT symmetry in quantum mechanics: A case study for the Scarf II potential

G. Lévai, M. Znojil

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72 Citations (Scopus)


Motivated by the duality of normalizable states and the presence of the quasi-parity quantum number q = ±1 in PT symmetric (non-Hermitian) quantum mechanical potential models, the relation of PT symmetry and supersymmetry (SUSY) is studied. As an illustrative example, the PT invariant version of the Scarf II potential is presented, and it is shown that the 'bosonic' Hamiltonian has two different 'fermionic' SUSY partner Hamiltonians (potentials) generated from the ground-state solutions with q = 1 and q = -1. It is shown that the 'fermionic' potentials cease to be PT invariant when the PT symmetry of the 'bosonic' potential is spontaneously broken. A modified PT symmetry inspired SUSY construction is also discussed, in which the SUSY charge operators contain the antilinear operator T. It is shown that in this scheme the 'fermionic' Hamiltonians are just the complex conjugates of the original 'fermionic' Hamiltonians, and thus possess the same energy eigenvalues.

Original languageEnglish
Pages (from-to)8793-8804
Number of pages12
JournalJournal of Physics A: Mathematical and General
Issue number41
Publication statusPublished - Oct 18 2002


ASJC Scopus subject areas

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

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