$[L_i,L_j]=i\hbar\epsilon_{ijk}L_k$, $[S_i,S_j]=i\hbar\epsilon_{ijk}S_k$, $[L_i,S_j]=0$, 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>.

Solution

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

 Solution (source code)