For two angular momenta of quantum numbers j₁ and j2, there are (2j1 + 1) × (2j2 + 1) possible products |j1,m,,)|j2,m₂) of eigenstates of the individual angular momenta. Count all the possible eigenstates lj,mj) of the total angular momentum, and show that there are exactly (2j1 + 1) × (2j2 + 1) such eigenstates.

For two angular momenta of quantum numbers j₁ and j2, there are (2j1 + 1) × (2j2 + 1) possible products |j1,m,,)|j2,m₂) of eigenstates of the individual angular momenta. Count all the possible eigenstates lj,mj) of the total angular momentum, and show that there are exactly (2j1 + 1) × (2j2 + 1) such eigenstates.