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Search Results for Collection: Computing and Mathematical Sciences Papers

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Second order superintegrable systems in conformally flat spaces. III. Three-dimensional classical structure theory

Kalnins, Ernie G.; Kress, Jonathan M.; Miller, W., Jr. (2005)

This paper is part of a series that lays the groundwork for a structure and classification theory of second-order superintegrable systems, both classical and quantum, in real or complex conformally flat spaces. Here we ...
Second order superintegrable systems in conformally flat spaces. II. The classical two-dimensional Stäckel transform

Kalnins, Ernie G.; Kress, Jonathan M.; Miller, W., Jr. (2005)

This paper is one of a series that lays the groundwork for a structure and classification theory of second order superintegrable systems, both classical and quantum, in conformally flat spaces. Here we study the Stäckel ...
Second-order superintegrable systems in conformally flat spaces. I. Two-dimensional classical structure theory

Kalnins, Ernie G.; Kress, Jonathan M.; Miller, W., Jr. (2005)

This paper is the first in a series that lays the groundwork for a structure and classification theory of second-order superintegrable systems, both classical and quantum, in conformally flat spaces. Many examples of such ...
Superintegrability on the two-dimensional hyperboloid

Kalnins, Ernie G.; Miller, W., Jr.; Pogosyan, G.S. (1997)

In this work we examine the basis functions for classical and quantum mechanical systems on the two-dimensional hyperboloid that admit separation of variables in at least two coordinate systems. We present all of these ...
Nonorthogonal R-separable coordinates for four-dimensional complex Riemannian spaces

Kalnins, Ernie G.; Miller, W., Jr. (1981)
Second-order superintegrable systems in conformally flat spaces. V. Two- and three-dimensional quantum systems

Kalnins, Ernie G.; Kress, Jonathan M.; Miller, W., Jr. (2006)

This paper is the conclusion of a series that lays the groundwork for a structure and classification theory of second-order superintegrable systems, both classical and quantum, in conformally flat spaces. For two-dimensional ...
Complete sets of invariants for dynamical systems that admit a separation of variables

Kalnins, Ernie G.; Kress, Jonathan M.; Miller, W., Jr.; Pogosyan, G.S. (2002)

Consider a classical Hamiltonian H in n dimensions consisting of a kinetic energy term plus a potential. If the associated Hamilton–Jacobi equation admits an orthogonal separation of variables, then it is possible to ...
The general theory of R-separation for Helmholtz equations

Kalnins, Ernie G.; Miller, W., Jr. (1983)

We develop the theory of R-separation for the Helmholtz equation on a pseudo-Riemannian manifold (including the possibility of null coordinates) and show that it, and not ordinary variable separation, is the natural analogy ...
Superintegrable systems in Darboux spaces

Kalnins, Ernie G.; Kress, Jonathan M.; Miller, W., Jr. (2003)

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 Darboux spaces of revolution that have ...
Mixed basis matrix elements for the subgroup reductions of SO(2,1)

Kalnins, Ernie G. (1973)

By using the irreducible decomposition on the two-dimensional light cone, the mixed basis matrix elements for the three subgroup reductions of SO(2,1) are calculated. These matrix elements are calculated for the principal ...