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

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

2010-10-10

arxiv.org/abs/1010.1909v1

Annals Phys.326:538-539,2011

Physics

Quantum Physics

2 pages

Scientific paper

10.1016/j.aop.2010.10.012

In "Comment on Supersymmetry, PT-symmetry and spectral bifurcation" \cite{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 \cite{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: $C^{PT}[2(A-B)+\alpha]=0$. It needs to be emphasized that in the models considered in \cite{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 \textit{independent} of the $sl(2)$ symmetry consideration for a large class of PT-symmetric potentials.

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