4. consider a particle constrained to move on the surface of a sphere of radius a. take the center of the sphere as the origin of coordinates. the potential is then of the form r a (a) give the hamiltonian operator for the particle in spherical coordinates, and write out the t-independent schroedinger equation. (b) to make life easy ignore the angular dependence of the potential, i. e., set u(0, o) uo, where uo is a constant. what are the energy levels?