Question
In Example 5.1 and Problem $5.5(\mathrm{b})$ we ignored spin (or, if you prefer, we assumed the particles are in the same spin state).
(a) Do it now for particles of spin $1 / 2$. Construct the four lowest-energy configurations, and specify their energies and degeneracies.
Suggestion: Use the notation $\psi_{n_{1} n_{2}}|s m\rangle,$ where $\psi_{n_{1} n_{2}}$ is defined in Example 5.1 and $| s m)$ in Section $4.4 .3 . ?$
(b) Do the same for spin 1. Hint. First work out the spin-1 analogs to the spin-1/2 singlet and triplet configurations, using the Clebsch-Gordan coefficients; note which of them are symmetric and which antisymmetric.