On “Comment on Supersymmetry, PT-symmetry and spectral bifurcation”

In “Comment on Supersymmetry, PT-symmetry and spectral bifurcation” 1], 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 2]. 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: C^PT2(A − B) + α] = 0. It needs to be emphasized that in the models considered in 2], 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.