Hierarchy of QM SUSYs on a Bounded Domain

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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15 pages, 3 figures

Scientific paper

10.1088/1751-8113/42/26/265203

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.

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