Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians

Al-Hashimi, M. H.; Salman, M.; Shalaby, A.; Wiese, U.-J. (2013). Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians. Annals of physics, 337, pp. 1-24. Elsevier 10.1016/j.aop.2013.06.002

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We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant.

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