Quantum Dynamics in Floquet Theory

of the Periodically Time-Dependent Harmonic Oscillator under a periodic forcing

A. Fedoul, A.L. Marrakchi, S. Sayouri*, A. Chatwiti

LPTA, Département de Physique, Faculté des Sciences-Dhar Mahraz

BP.1796 Fes-Atlas, Morocco

* Corresponding author. E-mail: ssayouri@ yahoo.com

Received: 25 June 2005; revised version accepted: 02 November 2005

Abstract

A solution of the Schrödinger equation is given for the periodical time-dependent harmonic oscillator, by using the Floquet representation and the resonating averages method. The explicit analytic expressions for the Floquet states and their corresponding wave functions are given. The formalism provides an efficiency tool for analyzing the various transition probabilities as well as the uncertainty relation of the system. The effect of a periodical external force on the Floquet states and the two-photon algebra realization are shortly discussed.

Keywords: Floquet theorem; Resonating Averages Method; Damping; Harmonic Oscillator.

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