Classical and quantum study of a generalized Kepler–Coulomb system

Abstract

AbstractThe nonrelativistic potential V = α/r + β cos θ/(r sin θ)2 + γ/(r sin θ)2, which constitutes an extension of the Kepler‐Coulomb potential and of the Hartmann potential, is investigated from both a classical and a quantum mechanical viewpoint. The corresponding Schrödinger equation is solved in parabolic coordinates by using the Kustaanheimo‐Stiefel transformation. The accidental degeneracy for the discrete spectrum is explained through the introduction of an su(2) dynamical invariance algebra. The Hamilton–Jacobi equation is solved in parabolic coordinates. The planarity and the periodicity of the trajectories are investigated. All finite trajectories are found to be quasi‐periodic (rather than periodic as in the case of the Kepler–Coulomb system). © 1993 John Wiley & Sons, Inc.