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Laplace-type equations as conformal superintegrable systems
E. G. Kalnins, J. M. Kress, W. Miller +1
We lay out the foundations of the theory of second-order conformal superintegrable systems. Such systems are essentially Laplace equations on a manifold with an added potential: $(…
Structure Theory for Second Order 2D Superintegrable Systems with 1-Parameter Potentials
Ernest G. Kalnins, Jonathan M. Kress, Willard Miller +1
The structure theory for the quadratic algebra generated by first and second order constants of the motion for 2D second order superintegrable systems with nondegenerate (3-paramet…
Models for Quadratic Algebras Associated with Second Order Superintegrable Systems in 2D
Ernest G. Kalnins, Willard Miller, Sarah Post
There are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symm…
Superintegrable Systems in Darboux spaces
E. G. Kalnins, J. M. Kress, W. Miller +1
Almost all research on superintegrable potentials concerns spaces of constant curvature. In this paper we find by exhaustive calculation, all superintegrable potentials in the four…