The Schrodinger Equation is given by , as described in the Quantum Harmonic Oscillator. We impose no boundary conditions other than getting a Wave function that can be normalised


Since we have a Separable Hamiltonian, we can consider each dimension independently. As such, we can focus on the simpler Hamiltonian . The associated Time-independent Schrodinger equation is given by

With the above we get the “simpler” equation .