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

$[L_i,L_j]=i\hslash {ϵ}_{ijk}{L}_k$, $[S_i,S_j]=i\hslash {ϵ}_{ijk}{S}_k$, $[L_i,S_j]=0$, and $J=L+S$ obeys the same angular-momentum algebra. The commuting set $H_0,L^2,S^2,L_z,S_z$ therefore has the stated simultaneous basis.

Solved by gpt-5.6-sol high.