Dirac equation in the foldy-wouthuysen representation describing the interaction of spin-1/2 relativistic particles with an external electromagnetic field

The Dirac equation in Foldy–Wouthuysen representation, describing the interaction between spin-1/2 relativistic particles and an external electromagnetic field has been obtained. It is valid for a weak field approximation. Derivatives of all orders with respect to the field potentials are taken into account in this equation, in distinction of the previous investigations. The quantum mechanical equation of spin motion in Foldy–Wouthuysen representation, agreeing with the classical Bargmann–Michel–Telegdi equation, has been found.