The Hamiltonian H represents the energy and dynamics of the system. In a spherically symmetric situation, the Hamiltonian is invariant under rotations: R H R − − 1 = H where R is a rotation operator. As a consequence, [ H , R ] = 0 , and then [ H , J ] = 0 due to the relationship between J and R. By the Ehrenfest theorem, it follows that J is conserved.