Exact solvability of superintegrable Benenti systems

Abstract

We establish quantum and classical exact solvability for two large classes of maximally superintegrable Benenti systems in $n$ dimensions with arbitrarily large $n$. Namely, we solve the Hamilton--Jacobi and Schrödinger equations for the systems in question. The results obtained are illustrated for a model with the cubic potential.

15 pages, LaTeX 2e, no figures; in the updated version a number of typos were fixed and other minor changes were made

References in corpus (8)

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• Superintegrability with third order invariants in quantum and classical mechanics
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• Superintegrability in a two-dimensional space of non-constant curvature
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Cited by in corpus (3)

• Superintegrability on N-dimensional curved spaces: Central potentials, centrifugal terms and monopoles
• Integrable quantum Stäckel systems
• Classical and Quantum Superintegrability of Stäckel Systems