Total Angular Momentum of Spin-½ Particles

V Hnizdo

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.

Robert A. Close

Paul L. Corio

Igor V. Komarov, R. Tarrach

We prove that for any nonrelativistic rotationally invariant two-particle quantum system whose interaction is velocity independent the total angular momentum of the ground state is bounded by the sum of the spins; i.e., ${j}_{\mathrm{max}={s}_{1}+{s}_{2}}$. .AE

Niels Geerits, Stephan Sponar

We demonstrate that spin-orbit coupled states are generated in neutral magnetic spin-1/2 particles traveling through an electric field. The quantization axis of the orbital angular momentum is parallel to the electric field; hence both longitudinal and transverse orbital angular momentum can be created. Furthermore, we show that the total angular momentum of the particle is conserved. Finally we propose a neutron optical experiment to measure the transverse effect.