PT-symmetric square well and the associated SUSY hierarchies

Abstract

The PT-symmetric square well problem is considered in a SUSY framework. When the coupling strength $Z$ lies below the critical value $Z_0^{(\mathrm{crit})}$ 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 $Z_0^{(\mathrm{crit})}$, there is a rich diversity of SUSY hierarchies, including some with PT-symmetry breaking and some with partial PT-symmetry restoration.

LaTeX, 18 pages, no figure; broken PT-symmetry case added (Sec. 6)

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• PT symmetric square well
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