A new approach on studying electron behavior under very intense laser beam

The recent emergence of the field studying interactions between very intense laser fields and charged particles, brings about the problem of determining if, and under what conditions, the quantum equations which describe these interactions are at the classical limit. We present an affirmative answer to this question in the case of an electron in electromagnetic field, corresponding to intensities of the electrical field of the order one atomic unit, or greater. We neglect the spin interactions, and show that with very good approximation (the relative error being less than 10^-7), the solution of the Klein-Gordon equation is a function only of the classical action S, written for the same system. Our approach does not use the semiclassical approximation, and it implies that the solution of the Klein-Gordon equation is at the classical limit of quantum mechanics for the systems discussed here. The results lead to a simplified computational model for analysing these systems.