Stäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics

Abstract

A non-degenerate second-order maximally conformally superintegrable system in dimension 2 naturally gives rise to a quadric with position dependent coefficients. It is shown how the system's Stäckel class can be obtained from this associated quadric.The Stäckel class of a second-order maximally conformally superintegrable system is its equivalence class under Stäckel transformations, i.e., under coupling-constant metamorphosis.

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Cited by in corpus (3)

• Superintegrable quantum mechanical systems with position dependent masses invariant with respect to two parametric Lie groups
• Integrable and superintegrable quantum mechanical systems with position dependent masses invariant with respect to one parametric Lie groups. 2. Systems with dilatation and shift symmetries
• Dynamical symmetry algebra of two superintegrable two-dimensional systems