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

Abstract

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.

Latex, 12 pages, Figures available from Authors, To appear in Physics Letters A. Please send requests for figures to [email protected] or [email protected]

References in corpus (4)

• Supersymmetry and Quantum Mechanics
• New Eaxactly Solvable Hamiltonians: Shape Invariance and Self-Similarity
• Exactly Solvable Potentials and Quantum Algebras
• New Shape Invariant Potentials in Supersymmetric Quantum Mechanics

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• New Solvable Singular Potentials
• Comment on "Supersymmetry and Singular Potentials" by Das and Pernice [Nucl. Phys. B 561 (1999) 357]
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• Algebraic Shape Invariant Potentials as the Generalized Deformed Oscillator
• A Venn diagram for supersymmetric, exactly solvable, shape invariant, and Infeld-Hull factorizable potentials
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