Hierarchy of QM SUSYs on a Bounded Domain

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.

15 pages, 3 figures

References in corpus (8)

• Making Sense of Non-Hermitian Hamiltonians
• Self-isospectrality, special supersymmetry, and their effect on the band structure
• Low-dimensional Supersymmetric Lattice Models
• A New Family of N-fold Supersymmetry: Type B
• Supersymmetry in 5d Gravity
• Gauge-Fixing and Residual Symmetries in Gauge/Gravity Theories with Extra Dimensions
• Quantization and Conformal Properties of a Generalized Calogero Model
• New supersymmetric partners for the associated Lame potentials