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

We demonstrate that the recent paper by Abhinav and Panigrahi entitled 'Supersymmetry, PT-symmetry and spectral bifurcation' [K. Abhinav, P.K. Panigrahi, 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 eigen-values, 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. (C) 2010 Elsevier Inc. All rights reserved.