The Hamiltonian for two particles with angular momentum quantum numbers
l1 = l2 = 1, is
\(\widehat{H}=\frac{\epsilon}{h^2}\left[\left(\hat{L}_1+\hat{L}_2\right) \cdot \hat{L}_2-\left(\hat{L}_{1 z}+\hat{L}_{2 z}\right)^2\right] \\\)
If the operator for the total angular momentum is given by \(\hat{L}=\hat{L}_1+\hat{L}_2\), then the possible energy eigenvalues for states with l = 2, (where the eigenvalues of \(\widehat{L}^2\) are l(l + 1)h2) are
1
3∈, 2∈, –∈
2
6∈, 5∈, 2∈
3
3∈, 2∈, ∈
4
–3∈, −2∈, ∈