From quantum to classical effects in interactions between electrons and very intense laser beams

We prove that the Schrodinger equation, written for a closed system composed of an electron and electromagnetic field, has a solution at the classical limit if the dipole approximation is fulfilled and the magnetic potential vector enters in classical form in the Schrodinger equation. Though the above property is valid generally in the case of laser beams, its potential importance is increased for the domain of the very high intensities of the electrical field, where it is in agreement with a lot of recent classical models and experimental results from literature. This result leads to a simplified computational model for the interaction between electrons and laser beams.