2. (a) Potential energy of a planar isotropic harmonic oscillator has the form U(x, y) = 2 - ( x2 + 12). (1) where m is the particle mass and w is the oscillation frequency. Determine the energy levels and stationary state wave functions using the method of separation of variables in rectangular (x,y) coordinates. Assume that the stationary state wave functions of the linear oscillator problem pose)(x) are given. What is the ground state energy? What is the degree of degeneracy of the energy levels? What is the parity of the energy states? (b) Please answer the same questions as in part (a) for a spherical harmonic oscillator whose potential energy has the form U(r) = _ mo-r2 (2) using the method of separation of variables in rectangular (x,);z) coordinates. FYI: the number of ways N balls can be distributed among 3 baskets is G(N) = (N+ 1 )(N +2) 2