ON THE FLOQUET STATES OF THE HARMONIC OSCILLATOR

WITH A TIME-DEPENDENT MASS OR/AND FREQUENCY

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 : azfe1@ caramail.com or ssayouri@ yahoo.com

Received : 1 May 2004; revised version accepted : 13 January 2005

Abstract

In this paper, we apply the Floquet theorem and the resonating averages method valid for periodical Hamiltonians. We solve the Schrödinger equation for the harmonic oscillator whose mass or frequency varies periodically with time. We determine its Floquet states as well as its corresponding wave functions. We give the various transition probabilities, and analyze the uncertainty relation. The effect on these states of a periodic external force is shortly examined.

Keywords: Floquet Theorem; Resonating Averages; Hamiltonian; Harmonic Oscillator.

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