Perturbation Calculation for H2 Energy Shift

We now calculate the expectation value of $H_2$. We will immediately use the fact that $j=\ell\pm{1\over 2}$.

$$\begin{eqnarray*} \left<\psi_{njm_j\ell s}\left\vert H_2\right\vert \psi_{njm_j\... ...] \qquad \matrix{ j=\ell + {1\over 2} \cr j=\ell -{1\over 2} } \end{eqnarray*}$$

Note that in the above equation, we have canceled a term ${\ell\over\ell}$ which is not defined for $\ell=0$. We will return to this later.