Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians |
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Authors: | MH Al-Hashimi M Salman A Shalaby U-J Wiese |
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Institution: | 1. Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern, Switzerland;2. Department of Mathematics, Statistics, and Physics, Qatar University, Al Tarfa, Doha 2713, Qatar;3. Physics Department, Faculty of Science, Mansoura University, Egypt;4. Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, USA |
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Abstract: | 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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Keywords: | Supersymmetry Self-adjoint extension Contact interaction Delta function potential Robin boundary condition |
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