Potentials with Two Shifted Sets of Equally Spaced Eigenvalues and Their Calogero Spectrum

Details Potentials with Two Shifted Sets of Equally Spaced Eigenvalues and Their Calogero Spectrum Potentials with Two Shifted Sets of Equally Spaced Eigenvalues and Their Calogero Spectrum

1996-11-12

arxiv.org/abs/hep-th/9611086v1

Phys.Lett. A224 (1996) 5-14

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 12 pages, Figures available from Authors, To appear in Physics Letters A. Please send requests for figures to agangop@l

Scientific paper

10.1016/S0375-9601(96)00807-9

Motivated by the concept of shape invariance in supersymmetric quantum mechanics, we obtain potentials whose spectrum consists of two shifted sets of equally spaced energy levels. These potentials are similar to the Calogero-Sutherland model except the singular term $\alpha x^{-2}$ always falls in the transition region $-1/4 < \alpha < 3/4$ and there is a delta-function singularity at x=0.

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