Volume 74, Number 6, June 2006
|Page(s)||1013 - 1019|
|Section||Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics|
|Published online||12 May 2006|
Indeterminacy of amplitude and phase variables in classical dynamical systems: The harmonic oscillator
Laboratorio de Optica Cuantica, Departamento de Fisica, Universidad A. Metropolitana Unidad Iztapalapa, Mexico D.F., Ap. Post. 55-534, Mexico
Corresponding author: firstname.lastname@example.org
Accepted: 13 April 2006
The amplitude and phase are shown to be variables that are not uniquely determined for the one-dimensional time-dependent harmonic-oscillator equation. Even when the parameter is time independent, it is shown that the amplitude and frequency may be time dependent and the phase nonlinear with respect to time. The consequences of this indeterminacy in the energy and the orthogonal-functions invariant are evaluated. The measurement of these quantities is discussed.
PACS: 45.30.+s – General linear dynamical systems / 45.50.Dd – General motion / 02.30.Hq – Ordinary differential equations
© EDP Sciences, 2006
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