Nonrelativistic Quantum Theory of an Electron in an Arbitrarily Intense Laser Field

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Abstract
An essentially exact treatment of the time‐dependent Schrödinger equation for a Bloch electron (or a free electron) in the presence of an arbitrarily intense laser field is described. Expressions for the wavefunction, current density, and energy of the electron state are presented in closed form for the case when the effective mass approximation is valid. The limitations of an ``almost exact'' solution of very simple form are investigated, the corrections to the almost exact solution being determined by the WKB approximation method. The exact solution for the wavefunction turns out to be quite different from that given by perturbation theory. However, the changes in the values of the current density and energy due to the presence of the laser field turn out to be, within the limitations imposed by the nonrelativistic nature of the Schrödinger theory, linear and quadratic in the field amplitude, and therefore agree with the results of perturbation theory.