Europhys. Lett.
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
Europhys. Lett., 74 (6), pp. 1013-1019 (2006)
DOI: 10.1209/epl/i2005-10592-1

Indeterminacy of amplitude and phase variables in classical dynamical systems: The harmonic oscillator

M. Fernández-Guasti

Laboratorio de Optica Cuantica, Departamento de Fisica, Universidad A. Metropolitana Unidad Iztapalapa, Mexico D.F., Ap. Post. 55-534, Mexico

received 25 August 2005; accepted in final form 13 April 2006
published online 12 May 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.

45.30.+s - General linear dynamical systems.
45.50.Dd - General motion.
02.30.Hq - Ordinary differential equations.

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