Quantum motion on the three-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 prolate elliptic and oblate elliptic coordinates. The oblate and prolate elliptic wavefunctions are constructed in terms of the hyperspherical and cylindrical wavefunctions. A perturbation theory for the elliptic wavefunctions in powers of the elliptic parameter is established. Finally, the interbasis expansions are used to set up path integral identities for the two ellipse-cylindrical coordinate systems on S-(3).