harmonic potential among two particles

hurz

Hello, guys. I need a little help here.

Two particles of mass m interact by an harmonic unidimensional potential:
V=(k/2)(x₁-x₂)², k>0

If the total linear momentum is null, which are the possible energies when:
a)the 2 particles are distinguishable
b)identical particles of spin 0
c)identical particles of spin 1/2, in a singlet state
d)identical particles of spin 1/2, in a triplet state

NB: "There's no need of doing calculations"

Thanks!