Quantum dynamics of the Stern-Gerlach (S-G) effect

Abstract.

A quantum dynamical treatment of the S-G effect, to the leading order in $|e|\sqrt{\hbar c}\equiv\sqrt{\alpha}$ for the electron, where $\alpha$ is the fine-structure constant, and for spin 1/2 charged particles (e.g., the proton), in general, leads to a unitary expression for the probability density on the observation screen, where the magnetic field has a controllable longitudinal uniform component along the initial average direction of propagation of the particle, in addition to a non-uniform, almost longitudinal, magnetic field lying in the plane defined by the quantization axis, in question, of the spin and the initial average direction of propagation.