Introduction to Quantum Mechanics · Problem 7.27

Time-Independent Perturbation Theory — David J. Griffiths

Physics — Quantum Mechanics · strong_field_zeeman_effect

Problem

Consider the (eight) n=2n = 2 states, ∣2 ℓ mℓ ms⟩|2\,\ell\,m_\ell\,m_s\rangle. Find the energy of each state, under strong-field Zeeman splitting. Express each answer as the sum of three terms: the Bohr energy, the fine-structure (proportional to α2\alpha^2), and the Zeeman contribution (proportional to μBBext\mu_B B_{\text{ext}}). If you ignore fine structure altogether, how many distinct levels are there, and what are their degeneracies?

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