Classical and quantum integrability in 3D systems

Abstract

In this contribution, we discuss three situations in which complete integrability of a three dimensional classical system and its quantum version can be achieved under some conditions. The former is a system with axial symmetry. In the second, we discuss a three dimensional system without spatial symmetry which admits separation of variables if we use ellipsoidal coordinates. In both cases, and as a condition for integrability, certain conditions arise in the integrals of motion. Finally, we study integrability in the three dimensional sphere and a particular case associated with the Kepler problem in $S^3$.

plenary talk on the Conference QTS-5, July 2007, Valladolid, Spain

References in corpus (7)

• Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere $S^2$ and the hyperbolic plane $H^2$
• Two families of superintegrable and isospectral potentials in two dimensions
• Intertwined isospectral potentials in an arbitrary dimension
• Maximal superintegrability on N-dimensional curved spaces
• Invariant classification of orthogonally separable Hamiltonian systems in Euclidean space
• Hydrogen atom as an eigenvalue problem in 3D spaces of constant curvature and minimal length
• Classical and quantum three-dimensional integrable systems with axial symmetry

Cited by in corpus (2)

• The quantum free particle on spherical and hyperbolic spaces: A curvature dependent approach
• The quantum free particle on spherical and hyperbolic spaces: A curvature dependent approach II