3. The spatial part of the ground state energy eigenfunction for a one-dimensional simple harmonic oscillator is bo(x) = (mw) ¹/4 e mw Consider a quantum particle of mass m that

moves in two dimensions under the influ- ence of a a spring force directed towards the origin, e.g. a simple harmonic oscillator potential (SHO2). (a) What is the Hamiltonian in this case? What is the time-independent Schrödinger equation? (b) Write down an expression for the spatial part of the ground-state energy eigenfunc- tion, poo(x, y). Show that it is correctly normalised (note the integral expressions at the top of the sheet).