Comment on "Comment on 'Supersymmetry, PT-symmetry and spectral bifurcation'"
Abstract
In "Comment on Supersymmetry, PT-symmetry and spectral bifurcation" BQ1, Bagchi and Quesne correctly show the presence of a class of states for the complex Scarf-II potential in the unbroken PT-symmetry regime, which were absent in AP. However, in the spontaneously broken PT-symmetry case, their argument is incorrect since it fails to implement the condition for the potential to be PT-symmetric: CPT[2(A-B)+α]=0. It needs to be emphasized that in the models considered in AP, PT is spontaneously broken, implying that the potential is PT- symmetric, whereas the ground state is not. Furthermore, our supersymmetry (SUSY)-based 'spectral bifurcation' holds independent of the sl(2) symmetry consideration for a large class of PT-symmetric potentials.
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