A SIMPLE APPROACH FOR THE PROBLEM OF THE HARMONIC OSCILLATOR WITH TIME-DEPENDENT MASS AND FREQUENCY
Y. Achkar, S. Sayouri*, A.L. Marrakchi
Laboratoire de Physique Théorique et Appliquée, Département de Physique,
Faculté des Sciences B. P. 1796, Fès-Atlas, Maroc
* Corresponding author. E-mail: firstname.lastname@example.org
Received: 24 November 2006; revised version accepted: 23 July 2007
Exact analytical solutions for the Harmonic oscillator with time-dependent mass and frequency are given. The resolution is based on an adequate transformation which lead to a symmetrical second order differential equations of the conjugate variables p(t) and q(t), and on the hypothesis which consists in making constant the coefficient (damping parameter) of the first derivatives of p(t) and q(t) in these equations. It is shown that the set of solutions obtained, depending on the domains of values of the above mentioned constant, are consistent with the solutions derived by other methods. Besides, expectation values of p(t) and q(t) are calculated which allows the verification of the Heisenberg uncertainty principle.
Keywords : Harmonic oscillator ; Coherent states ; Expectation values