The anomalous Zeeman effect arises because electron spin contributes twice as much magnetic moment per angular momentum unit (g_s ≈ 2 from Dirac theory). The full energy shift is ΔE = g_J · μ_B · B · m_J where the Landé g-factor g_J = 1 + [J(J+1) + S(S+1) - L(L+1)] / [2J(J+1)] encodes the LS coupling. With B=0 there are 2J+1 degenerate m_J sublevels; B lifts this degeneracy into 2J+1 equally spaced levels. Selection rules ΔJ=0,±1 and Δm_J=0,±1 produce the characteristic multiplet pattern with spacing proportional to g_J·μ_B·B.