167 citations · 309 across the 8 of their papers we have counts for
8 papers
Toward Classification of 2nd Order Superintegrable Systems in 3-Dimensional Conformally Flat Spaces with Functionally Linearly Dependent Symmetry Operators
Bjorn K. Berntson, Ernest G. Kalnins, Willard Miller
We make significant progress toward the classification of 2nd order superintegrable systems on 3-dimensional conformally flat space that have functionally linearly dependent (FLD)…
Separation equations for 2D superintegrable systems on constant curvature spaces
M. A. Escobar-Ruiz, E. G. Kalnins, W. Miller
Second-order conformal quantum superintegrable systems in 2 dimensions are Laplace equations on a manifold with an added scalar potential and independent 2nd order conformal sy…
Structure results for higher order symmetry algebras of 2D classical superintegrable systems
E. G. Kalnins, W. Miller
Recently the authors and J.M. Kress presented a special function recurrence relation method to prove quantum superintegrability of an integrable 2D system that included explicit co…
Families of classical subgroup separable superintegrable systems
E. G. Kalnins, J. M. Kress, W. Miller
We describe a method for determining a complete set of integrals for a classical Hamiltonian that separates in orthogonal subgroup coordinates. As examples, we use it to determine…
Superintegrability and higher order constants for classical and quantum systems
E. G. Kalnins, W. Miller, G. S. Pogosyan
We extend recent work by Tremblay, Turbiner, and Winternitz which analyzes an infinite family of solvable and integrable quantum systems in the plane, indexed by the positive param…
Coupling constant metamorphosis and Nth order symmetries in classical and quantum mechanics
E. G. Kalnins, W. Miller, S. Post
We review the fundamentals of coupling constant metamorphosis (CCM) and the Stäckel transform, and apply them to map integrable and superintegrable systems of all orders into other…