Relativistic Stern-Gerlach Deflection: Hamiltonian Formulation

TL;DR

This paper develops a Hamiltonian framework to analyze the deflection of relativistic spin-polarized particles in magnetic and electric field gradients, and briefly explores spin-orbit coupling in nonrelativistic atomic systems.

Contribution

It introduces a Hamiltonian formalism for relativistic Stern-Gerlach effects and extends the analysis to spin-orbit coupling in atomic physics, providing a unified theoretical approach.

Findings

Hamiltonian formalism clarifies relativistic Stern-Gerlach deflection

Analysis of spin-orbit coupling in hydrogen-like atoms

Provides a basis for future experimental and theoretical studies

Abstract

A Hamiltonian formalism is employed to elucidate the effects of the Stern-Gerlach force on beams of relativistic spin-polarized particles, for passage through a localized region with a static magnetic or electric field gradient. The problem of the spin-orbit coupling for nonrelativistic bounded motion in a central potential (hydrogen-like atoms, in particular) is also briefly studied.