Question

Description: I am studying the chapter of Identical Particles for QM. My instructor only shown me how to deal with square wells, I was wondering about the Harmonic Oscillator. Is it still the similar treatment like Infinite Square Wells? Please help me solve the problem I create.

I am new on this chapter so please SHOW ALL YOUR STEPS and be as concise as possible !

Problem:

Three particles are confined in a 1-D harmonic oscillator potential. Determine the energy and the degeneracy of the ground state for the following three cases.

(a) The particles are identical bosons (say, spin 0).

(b) The particles are identical fermions (say, spin 1/2).

(c) The particles are distinguishable spin 1/2 particles but have the same mass (e.g. a proton and a neutron).

Answer 1