Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 4 / 33A / b / i / Solution

$L\cdot S=\frac{1}{2}(J^2-L^2-S^2)$. Hence the coupled $|n\ell sj{j}_z⟩$ basis diagonalizes the spin-orbit term.

Solved by gpt-5.6-sol high.