  In nonrelativistic quantum mechanics, the total (i.e. orbital plus spin)
angular momentum of a charged particle with spin that moves in a Coulomb plus
spin-orbit-coupling potential is conserved. In a classical nonrelativistic
treatment of this problem, in which the Lagrange equations determine the
orbital motion and the Thomas equation yields the rate of change of the spin,
the particle's total angular momentum in which the orbital angular momentum is
defined in terms of the kinetic momentum is generally not conserved. However, a
generalized total angular momentum, in which the orbital part is defined in
terms of the canonical momentum, is conserved. This illustrates the fact that
the quantum-mechanical operator of momentum corresponds to the canonical
momentum of classical mechanics.
