Self-Isospectral Periodic Potentials and Supersymmetric Quantum Mechanics

Details Self-Isospectral Periodic Potentials and Supersymmetric Quantum Mechanics Self-Isospectral Periodic Potentials and Supersymmetric Quantum Mechanics

1997-06-02

arxiv.org/abs/hep-th/9706012v1

Phys.Rev. D57 (1998) 1271-1276

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, ReVTeX, 6 figures, uses epsf

Scientific paper

10.1103/PhysRevD.57.1271

We discuss supersymmetric quantum mechanical models with periodic potentials. The important new feature is that it is possible for both isospectral potentials to support zero modes, in contrast to the standard nonperiodic case where either one or neither (but not both) of the isospectral pair has a zero mode. Thus it is possible to have supersymmetry unbroken and yet also have a vanishing Witten index. We present some explicit exactly soluble examples for which the isospectral potentials have identical band spectra, and which are ``self-isospectral'' in the sense that the potentials have identical shape, but are translated by one half period relative to one another.

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