Q6:1 A two-dimensional harmonic oscillator has a quantum hamiltonian operator H given by 1 H = 2m dx² ™ dy² 2m (dz + ay) +mw² (z° + y*). Write down the time independent Schrödinger equation for this oscillator. (i) Show that the Schrödinger equation for this H can be written as two one-dimensional equations by explicit separation of variables.

Q6:1 A two-dimensional harmonic oscillator has a quantum hamiltonian operator H given by 1 H = 2m dx² ™ dy² 2m (dz + ay) +mw² (z° + y*). Write down the time independent Schrödinger equation for this oscillator. (i) Show that the Schrödinger equation for this H can be written as two one-dimensional equations by explicit separation of variables.