Time-dependent conserved operators for autonomous systems and quantization of resistance

Abstract Two systems for a charged particle are studied using an adaptation of Lewis and Riesenfeld invariant method. The first system involves a particle under the effect of a constant electric field, and the second system adds a parallel magnetic field. In both cases, time-dependent conserved operators are identified, which can be used to derive time-dependent wave functions for the Schrödinger equation, where the time variable is not separable from the space coordinates. These conserved operators are also used to construct unitary operators, which define the symmetries of the systems. Finally, it is shown that the invariance of the wave function under the action of these unitary operators leads to the quantization of resistance equal to an integer number times the Klitzing’s constant.