167 citations · 419 across the 10 of their papers we have counts for
10 papers
Special function models of indecomposable representations: The Laguerre Case
Sébastien Bertrand, Ian Marquette, Willard Miller +1
In this paper, we point out connections between certain types of indecomposable representations of and generalizations of well-known orthogonal polynomials. Those represent…
Particle in a field of two centers in prolate spheroidal coordinates: integrability and solvability
Willard Miller, Alexander V Turbiner
We analyze one particle, two-center quantum problems which admit separation of variables in prolate spheroidal coordinates, a natural restriction satisfied by the H molecular…
Extended Kepler-Coulomb quantum superintegrable systems in 3 dimensions
E. G. Kalnins, J. M. Kress, W. Miller
The quantum Kepler-Coulomb system in 3 dimensions is well known to be 2nd order superintegrable, with a symmetry algebra that closes polynomially under commutators. This polynomial…
Superintegrability in a non-conformally-flat space
E. G. Kalnins, J. M. Kress, W. Miller
Superintegrable systems in two- and three-dimensional spaces of constant curvature have been extensively studied. From these, superintegrable systems in conformally flat spaces can…
Superintegrability and higher order constants for quantum systems
E. G. Kalnins, J. M. Kress, W. Miller
We refine a method for finding a canonical form for symmetry operators of arbitrary order for the Schroedinger eigenvalue equation on any 2D Riemannian manifold, real or complex, t…
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…