(Solved): In a hydrogen atom, the proton is stationary at the origin of the coordinates and its spin is given ...

In a hydrogen atom, the proton is stationary at the origin of the coordinates and its spin is given by ${\vec{S}}_1=S_1\hat{z}$. The electron has spin ${\vec{S}}_2=S_2\hat{z}$. The potential energy of the hyperfine interaction (spin-spin) is given per $U=\frac{{?}_0{q}_1{q}_2}{2?m_1{m}_2{r}_1^3}{\vec{S}}_1?{\vec{S}}_2$ where $M_1,q_1$ and $m_2,q_2$ are the masses and charges (in modulus) of the proton and the electron. Calculate the possible electron energy values.