Exact solvability of superintegrable Benenti systems
classification
🌊 nlin.SI
math-phmath.MP
keywords
systemsbenentiexactlargesolvabilitysuperintegrablearbitrarilyclasses
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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 Schr\"odinger equations for the systems in question. The results obtained are illustrated for a model with the cubic potential.
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