Physics – Mathematical Physics
Scientific paper
2010-07-22
Annals Phys.326:534-537,2011
Physics
Mathematical Physics
6 pages, no figure, published version
Scientific paper
10.1016/j.aop.2010.10.007
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.
Bagchi Bhaskar
Quesne Christiane
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