Problem 1. Consider the Hamiltonian of a mass m. particle subjected to an isotropic 3dimensional harmonic oscillator potential, namely VIZ-r} = %mw2r2_l as a function of the distance r from a xed center. [a] Show that the timeindependent Schrodinger equation is separable in spherical coordinates, and write the separated ordinary differential equa tions in r? l9, qt}. (b) Taking the orbital angular momentum quantum number of the system to be 5' = 1, nd the exact lowest energy solution for this E = 1 case, and show that a function of the following form obeys the rescaled radial Schrodinger equation: u[r} = Tar-r} = awe-01"\