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In the quantum result for spin I=1 we have a splitting into two levels when Vzz is different from zero these are the levels corresponding to m=+-1 and m=0. Such a case corresponds to the splitting of energy levels for the situation in which the nucleus (two positive charges) in toy model 0 is positioned perpendicularly to the electron axis (lie in xy plane perpendicular to z) and the situation in which the nucleus is positioned along z. Thus these situations are indistinguishable as long as d>>l because then the solution obtained from the first perturbation theory is almost consistent with the exact solution in toy model. It should be noted that intermediate situations for which the nucleus lies in intermediate directions in toy model are not forbidden on the grounds of quantum mechanics, we do not consider them in the given answer.
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