Comment on `Supersymmetry, PT-symmetry and spectral bifurcation'

Abstract

We demonstrate that the recent paper by Abhinav and Panigrahi entitled `Supersymmetry, PT-symmetry and spectral bifurcation' [Ann.\ Phys.\ 325 (2010) 1198], which considers two different types of superpotentials for the PT-symmetric complexified Scarf II potential, fails to take into account the invariance under the exchange of its coupling parameters. As a result, they miss the important point that for unbroken PT-symmetry this potential indeed has two series of real energy eigenvalues, to which one can associate two different superpotentials. This fact was first pointed out by the present authors during the study of complex potentials having a complex $sl(2)$ potential algebra.

arXiv comment6 pages, no figure, published version

References in corpus (7)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• sl(2, C) as a complex Lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues
• Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework
• Generating Complex Potentials with Real Eigenvalues in Supersymmetric Quantum Mechanics
• Complexified PSUSY and SSUSY interpretations of some PT-symmetric Hamiltonians possessing two series of real energy eigenvalues
• Supersymmetry, PT-symmetry and Spectral Bifurcation

Cited by in corpus (3)

• Parametric symmetries in exactly solvable real and P T symmetric complex potentials
• Self-isospectral tri-supersymmetry in PT-symmetric quantum systems with pure imaginary periodicity
• Linked $\mathcal{P}\mathcal{T}$-symmetry to Supersymmetry in a class of non-Hermitian Hamiltonians