Скачать или смотреть Derivation of Magnetic Moment & Landé g-factor in LS Coupling | Magnetic Moment in LS Coupling

The magnetic moment µJ of an atom in which LS coupling holds has the magnitude
µJ=√J(J+1)gjµB
where µB=eħ/2m is the Bohr magneton and gj=1+J(J+1)-L(L+1)+S(S+1)/2J(J+1)

is the Landé g factor. (a) Derive this result with the help of the law of cosines starting from the fact that averaged over time, only the components of µL and µS parallel to µJ contribute to J. (b) Consider an atom that obeys LS coupling that is in a weak magnetic field B in which the coupling is preserved. How many substates are there for a given value of J? What is the energy difference between different substates?
Step-by-step solution to Problem 37 of Chapter 7 from Arthur Beiser’s "Concepts of Modern Physics.”

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