Problem: Consider a harmonic oscillator of mass m undergoing harmonic motion in two dimensions x and y. The potential energy is given by V(x,y) = (1/2)kxx2 + (1/2)kyy2. (a) Write down the expression for the Hamiltonian operator for such a system. (b) What is the general expression for the allowable energy levels of the two-dimensional harmonic oscillator? (c) What is the energy of the ground state (the lowest energy state)? Hint: The Hamiltonian operator can be written as a sum of operators. Now I'm a bit lost on how to write the expression for the Hamiltonian. Is the Hamiltonian simply H = - h2/2m d2/dx2 + V(x,y) [where V(x,y) is given above]? Then with that Hamiltonian, solving the Schrodinger eqn is pretty straightforward to get H*psi = E*psi, now I'm a bit lost here as well to solve for the general expression for the allowable energy levels?