What is the degeneracy of the ground state

[JohanL]

$$H=\frac{p^2}{2m'}+V_0(r)+V(r)$$

where

$$V(r)=2[3\frac{(S \cdot r)^2}{r^2}-S^2]$$

and V_0(r) is a rotationally invariant potential, p=p1-p2, the relative momentum and m' the reduced mass. S=S1+S2 spin operator.

Assume first that V(r) is zero; what is the degeneracy of the ground state assuming that each of the dipoles are spin 1/2. After turning on V(r) how is the degeneracy split; what are the "quantum numbers" i.e. eigenvalues J and S of those new states.

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Any hints on how to start on a problem like this?

 

[JohanL]

Whats confusing me is how to handle

p^2 |a>

V_0 |a>

 

[JohanL]

I solved it