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