Adding Potentials to Superintegrable Systems with Symmetry

Abstract

In previous work, we have considered Hamiltonians associated with 3 dimensional conformally flat spaces, possessing 2, 3 and 4 dimensional isometry algebras. Previously our Hamiltonians have represented free motion, but here we consider the problem of adding potential functions in the presence of symmetry. Separable potentials in the 3 dimensional space reduce to 3 or 4 parameter potentials for Darboux-Koenigs Hamiltonians. Other 3D coordinate systems reveal connections between Darboux-Koenigs and other well known super-integrable Hamiltonians, such as the Kepler problem and isotropic oscillator.

22 pages, 3 tables. arXiv admin note: text overlap with arXiv:1910.08836

References in corpus (4)

• Superintegrable Systems in Darboux spaces
• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Superintegrability on N-dimensional curved spaces: Central potentials, centrifugal terms and monopoles
• Quantum Super-Integrable Systems as Exactly Solvable Models

Cited by in corpus (3)

• Algebraic approach and exact solutions of superintegrable systems in 2D Darboux spaces
• Integrable and Superintegrable Extensions of the Rational Calogero-Moser Model in 3 Dimensions
• Algebraic structures and Hamiltonians from the equivalence classes of 2D conformal algebras