Interaction between two-dimensional quantum oscillators and time-dependent forces: Case of a harmonic force

We solve analytically the time dependent Schrödinger equation of a two-dimensional quantum oscillator subjected to a time-varying force. We apply the results to the case of a linearly and circularly polarized harmonic force. The main result is that the quantum oscillator orbit center performs a two-dimensional closed loop (elliptical) driven by the force. This theory has been specifically applied to the problem of a two-dimensional electron system subjected to a static and uniform magnetic field and radiation to explain the striking effects of radiation-induced magnetoresistance oscillations and zero resistance states.