Isospectrality of conventional and new extended potentials, second-order supersymmetry and role of PT symmetry

Abstract

We develop a systematic approach to construct novel completely solvable rational potentials. Second-order supersymmetric quantum mechanics dictates the latter to be isospectral to some well-studied quantum systems. $\mathcal{P}\mathcal{T}$ symmetry may facilitate reconciling our approach to the requirement that the rationally-extended potentials be singularity free. Some examples are shown.

13 pages, no figure, some additions to introduction and conclusion, 4 more references; to be published in Special issue of Pramana - J. Phys

References in corpus (1)

• An extended class of orthogonal polynomials defined by a Sturm-Liouville problem

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