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For the Hamiltonian [itex] H=\frac{P^2}{2\mu} -\frac{Ze^2}{r}+ \frac{\alpha}{r^3} L.S[/itex] (which we can use [itex] L.S=\frac{1}{2} (J^2-L^2-S^2)[/itex]in the third term) how to realize that the third term,[itex]\frac{\alpha}{r^3} L.S[/itex], commutes with sum of the first two terms,[itex] \frac{P^2}{2\mu} -\frac{Ze^2}{r}[/itex], and then conclude that the set of the operators [itex] J^2, J_z, L^2, S^2[/itex] are the best to work with? ([itex] \alpha, Z, e, \mu[/itex] are constants)

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# How to select the good basis for the special Hamiltonian?

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