Harmonic oscillator subject to parametric pulses: an amplitude (Milne) oscillator approach

harmonic oscillator subject to a parametric pulse is examined. The aim of t he paper is to present a new theory for analysing transitions caused by par ametric pulses. The new theoretical notions which are introduced relate the pulse parameters in a direct way with transition matrix elements. The harmonic-oscillator transitions are expressed in terms of the asymptoti c properties of a companion oscillator, the Milne (amplitude) oscillator. A traditional phase-amplitude decomposition of the harmonic-oscillator solut ions results in the so-called Milne's equation fur the amplitude, and the p hase is determined by an exact relation to the amplitude. This approach is extended in the present analysis with new relevant concepts and parameters for pulse dynamics of classical and quantal systems. The amplitude oscillator has a particularly nice numerical behaviour. In th e case of strong pulses it does not possess any of the fast oscillations in duced by the pulse on the original harmonic oscillator. Furthermore, the ne w dynamical parameters introduced in this approach are closely related to t he relevant characteristics of the pulse. The relevance to quantum mechanical problems such as reflection and transmi ssion from a localized well and the mechanical problem of controlling vibra tions is illustrated.