Quantum superintegrability and exact solvability in N dimensions

Abstract

A family of maximally superintegrable systems containing the Coulomb atom as a special case is constructed in N-dimensional Euclidean space. Two different sets of N commuting second order operators are found, overlapping in the Hamiltonian alone. The system is separable in several coordinate systems and is shown to be exactly solvable. It is solved in terms of classical orthogonal polynomials. The Hamiltonian and N further operators are shown to lie in the enveloping algebra of a hidden affine Lie algebra.

References in corpus (2)

• Completeness of superintegrability in two-dimensional constant curvature spaces
• Superintegrability in a two-dimensional space of non-constant curvature

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