QUANTUM MOTION ON THE 3-DIMENSIONAL SPHERE - THE ELLIPSO-CYLINDRICAL BASES

We study the free quantum motion on the three-dimensional sphere S-(3) in ellipsocylindrical coordinates, where we distinguish between prola te elliptic and oblate elliptic coordinates. The oblate and prolate el liptic wavefunctions are constructed in terms of the hyperspherical an d cylindrical wavefunctions. A perturbation theory for the elliptic wa vefunctions in powers of the elliptic parameter is established. Finall y, the interbasis expansions are used to set up path integral identiti es for the two ellipse-cylindrical coordinate systems on S-(3).