Analytical wave function of an atomic electron under the action of a powerful ultrashort electromagnetic field pulse

The interaction of atomic systems with high-power ultrashort electromagnetic field pulses (USPs) is currently the subject of many theoretical and experimental studies. However, a wave function has yet to be developed for the atomic electron located in such fields, including relativistic fields. In this Letter, an equation is obtained that is similar to the Schrödinger equation for the fields under consideration, but which takes into the account relativistic effects in powerful spatially inhomogeneous fields of USPs. Using the sudden disturbance approximation, an exact solution of the resulting equation is obtained in the form of an analytical wave function which is suitable for any type and form of ultrashort pulse, and which takes into account its magnetic component. It is shown that the obtained wave function satisfies the necessary completeness condition in quantum mechanics.