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PT-symmetric square well and the associated SUSY hierarchies

B. Bagchi·S. Mallik·C. Quesne
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Abstract

The PT-symmetric square well problem is considered in a SUSY framework. When the coupling strength $Z$ lies below the critical value $Z_0^{\rm (crit)}$ where PT symmetry becomes spontaneously broken, we find a hierarchy of SUSY partner potentials, depicting an unbroken SUSY situation and reducing to the family of $\sec^2$-like potentials in the $Z \to 0$ limit. For $Z$ above $Z_0^{\rm (crit)}$, there is a rich diversity of SUSY hierarchies, including some with PT-symmetry breaking and some with partial PT-symmetry restoration.

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B. Bagchi, S. Mallik, C. Quesne. 2002-07-01. PT-symmetric square well and the associated SUSY hierarchies. https://doi.org/10.1142/s0217732302008009

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