Kapitza-Dirac effect: Classical and quantum regimes

The Kapiza-Dirac effect (scattering of electrons by a standing light wave) is described in terms of the quantum-mechanical and classical description of electrons. In the quantum-mechanical theory the initial wave function of an electron is taken either in the form of a single plane wave or a finite-size wave packet. In all cases, the average angle of scattering and the distribution function of scattered electrons are found. The results of the classical and single-plane wave quantum-mechanical descriptions are shown to differ from each other. The conditions of their applicability are determined with the help of the wave-packet theory.