The Quantum Mechanical Extension of the Boltzmann Equation

It is shown that the method of Kohn and Luttinger may be applied to obtain a generalized Boltzmann equation, for electrons in a solid, when the driving field has nonzero wavevector as well as frequency. By means of this equation, the behavior of the electrons in response to the field may be followed from the quasi-classical limit at small rates of change to the quantal limit at large rates of change.