Comment on the Solution of the Schrödinger Equation for a Nonrelativistic Electron in the Presence of Both a Periodic Crystal Potential and Monochromatic Laser Radiation

Abstract

Using the translational invariance properties of the total Hamiltonian, the solution of the time-dependent Schrödinger equation for an electron in a simple cubic lattice and in the presence of arbitrarily intense monochromatic laser radiation is shown to be equivalent to solving an ordinary second-order differential equation with one independent variable, provided the wavelength of the laser radiation is very large compared to the lattice spacing of the crystal.