Introduction to Quantum Mechanics · Problem 7.28

Time-Independent Perturbation Theory — David J. Griffiths

Physics — Quantum Mechanics · zeeman_effect_l_equals_zero

Problem

If ℓ=0\ell = 0, then j=sj = s, mj=msm_j = m_s, and the "good" states are the same (∣n ms⟩|n\,m_s\rangle) for weak and strong fields. Determine EZ1E^1_Z (from Equation 7.74) and the fine structure energies (Equation 7.69), and write down the general result for the ℓ=0\ell = 0 Zeeman effect—regardless of the strength of the field. Show that the strong-field formula (Equation 7.86) reproduces this result, provided that we interpret the indeterminate term in square brackets as 1.

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