One source of spin–orbit coupling in the Schrödinger representation

Abstract

The origin of spin–orbit coupling has been investigated in the Schrödinger picture with the constraint of Galilean invariance. A Lagrangian has been constructed with this group symmetry which contains a term that has been interpreted as the damping of the translational motion of the electron in a spinor field. From the Lagrangian a Hamiltonian [Formula: see text] has been formed by classical methods. A unitary transformation has been found which transforms [Formula: see text] into a Hamiltonian [Formula: see text] which contains not only the Zeeman terms, with the correct magnetic moment, but also the spin–orbit coupling.