PATH INTEGRAL QUANTIZATION OF CERTAIN NONCENTRAL SYSTEMS WITH DYNAMIC SYMMETRIES

Path integral quantization is done for the five classes of potentials appearing in the systematic search for nonrelativistic systems with dynamical symmetries done by Makarov, Smorodinsky, Valiev, and Winternitz [Nuovo Cimento A 52, 1061 (1967)]. By an iterated application of Bateman's series formula to the polar coordinate path integral, an expansion is obtained on the Feynman kernel or the Green's function, whichever is possible, in terms of hypergeometric functions of the polar and azimuthal parts and a radial path integral is obtained whose evaluation yields the energy eigenvalues and the normalized wave functions. Special cases include the Hartmann potential and the ring-shaped oscillator.