Supersymmetric Descendants of Self-Adjointly Extended Quantum Mechanical Hamiltonians
arXiv:1303.2343 · doi:10.1016/j.aop.2013.06.002
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.
31 pages, 10 figures
References in corpus (4)
- From a Particle in a Box to the Uncertainty Relation in a Quantum Dot and to Reflecting Walls for Relativistic Fermions
- Casimir effect for the scalar field under Robin boundary conditions: A functional integral approach
- Self-adjoint Extensions for Confined Electrons:from a Particle in a Spherical Cavity to the Hydrogen Atom in a Sphere and on a Cone
- Harmonic Oscillator in a 1D or 2D Cavity with General Perfectly Reflecting Walls