Dynamical invariance algebra of the Hartmann potential

Abstract

The 'accidental' degeneracy occurring in the quantum mechanical treatment of the ring-shaped potential V=- eta sigma 2r-1+1/2q eta 2 sigma 2(r sin theta )-2 is explained by constructing an su(2) dynamical invariance algebra. The Schrodinger equation is solved in parabolic coordinates written in the framework of the Kustaanheimo-Stiefel transformation and the Hamilton-Jacobi equations are solved in ordinary parabolic coordinates. All finite trajectories are found to be periodic.