Do part b just Consider the Hamiltonian for a hydrogen-like atomp2H =+ V(r)+:2meS.L dV(r)2merdrwhere V(r) =-Za/r, Z is the atomic number. We can take the convenience bysetting ħ = c = 1, hence the fine structure constant a =4T eg fica. We know the eigenvalue and eigenstate of hydrogen area?meEne =|Wnem) = |Rn,e)|em),2(n, + l+1)2'with n = n, + l+1. But with the newly added spin-orbit coupling, it is betterto move in SL-coupling representation. Construct the eigenstates for{H, J², Jz, L²} with the eigenstates of hydrogen.b. Find the energy level splitting by spin-orbital coupling (you can utilizeHellmann-Feynman theorem for the expectation values instead of integration).

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Answered: b. Find the energy level splitting by…

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b. Find the energy level splitting by spin-orbital coupling (you can utilize Hellmann-Feynman theorem for the expectation values instead of integration).