Completeness of superintegrability in two-dimensional constant-curvature spaces

By E. Kalnins, J. Kress, G. Pogosyan, Willard Miller. 2001

164 citations recorded by the source corpus.

We classify the Hamiltonians H = px2 + py2 + V(x,y) of all classical superintegrable systems in two-dimensional complex Euclidean space with two additional second-order constants of the motion. We similarly classify the superintegrable Hamiltonians H = J12 + J22 + J32 + V(x, y, z) on the complex two-sphere where x2 + y2 + z2 = 1. This is achieved in all generality using properties of the complex Euclidean group and the complex orthogonal group.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/2fe03f41ef935d1abe9ae28c0e76298ef9029af8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. P. Winternitz
2. Willard Miller Jr.

Citations in the corpus

• Superintegrable systems in Darboux spaces (2003, background): “Systematic studies of superintegrable systems have been conducted in spaces of constant curvature in two dimensions [3, 4, 5, 6, 7].”