The Hamiltonian of an electron stuck within a tunnel in a dialectic cube is found to be
Find the possible energies and corresponding wavefunctions of H. Write an expression for the ground state energy and normalized wavefunction.
I tried plugging this Hamiltonian into the Schrodinger Equation and completing the square, but then I get an impossible differential equation. Is this the right thing to do? If it is, how do I solve for the ground state energy and the normalized wavefunction? Any help would be welcome--I am really confused by this problem.