Hierarchy of QM SUSYs on a bounded domain

2008/12/26 by Tomoaki Nagasawa, Satoshi Ohya, Kazuki Sakamoto +2
Mathematics · Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #hep-th #quant-ph

paper · pdf · doi:10.1088/1751-8113/42/26/265203

published as J.Phys.A42:265203,2009 · 15 pages, 3 figures

arxiv created 2008/12/26 · openalex publication_date 2009/06/08 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We systematically formulate a hierarchy of isospectral Hamiltonians in one-dimensional supersymmetric quantum mechanics on an interval and on a circle, in which two successive Hamiltonians form N=2 supersymmetry. We find that boundary conditions compatible with supersymmetry are severely restricted. In the case of an interval, a hierarchy of, at most, three isospectral Hamiltonians is possible with unique boundary conditions, while in the case of a circle an infinite tower of isospectral Hamiltonians can be constructed with two-parameter family of boundary conditions.

Citations

• New supersymmetric partners for the associated Lamé potentials
• Making Sense of Non-Hermitian Hamiltonians
• Supersymmetry and discrete transformations on S1 with point singularities
• Hidden supersymmetry in quantum bosonic systems
• Gauge fixing and residual symmetries in gauge/gravity theories with extra dimensions
• The generalized point interaction in one dimension
• A new family of N-fold supersymmetry: type B
• Supersymmetry and Quantum Mechanics