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American Journal of Physics

Quantum dynamics and a semiclassical description of the photon

Giles Henderson

Published Aug 1, 1980• 6 citations
Publisher

Abstract

Nonstationary, superposition wave functions are used with computer graphics to reveal the dynamic quantum trajectories of several molecular and electronic transitions. These methods are then coupled with classical electromagnetic theory to provide a conceptually clear picture of the emission process and emitted radiation localized in time and space.

DOI
10.1119/1.12328

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Nonstationary, superposition wave functions are used with computer graphics to reveal the dynamic quantum trajectories of several molecular and electronic transitions. These methods are then coupled with classical electromagnetic theory to provide a conceptually clear picture of the emission process and emitted radiation localized in time and space.
The relationship between the diverging of classical trajectories in chaotic many-body systems, the spreading of quantum wave packets, and the validity and use of classical molecular dynamics is explored. This analysis, which is based on the semiclassical description of wave function propagation in terms of a weighted integration over a traveling fixed width coherent state basis, suggests that the exponential divergence of nearby classical trajectories in chaotic many-body systems should result in the rapid delocalization of an initially localized quantum wave packet describing the state of the system. Thus the justification for the use of classical molecular dynamics procedures for these supposedly classical systems cannot be based on the picture of the system wave function remaining localized as its center follows a nearly classical trajectory. The quantum evolution of the system density, on the other hand, requires two propagators, and each of these propagators is represented as an integration over trajectories in the semiclassical picture. The interference between the contributions from these two integrations over classical trajectories focuses the analysis on the most important points in this trajectory pair space, which are shown to occur when both trajectories in the pair are the same. Given reasonable assumptions for the initial density for a system that is expected to be well described by classical molecular dynamics, and given an appropriate choice for the width of the coherent state basis which is employed in the semiclassical description, it is shown that the semiclassical expressions for time dependent observables and correlation functions reduce the purely classical expressions, despite the fact that an initially localized wave packet would rapidly delocalize for the same system.
The photoelectric effect, the Compton effects, and now anticorrelation experiments have been claimed to prove that light consists of particles flying through a void. However the particle model is decisively falsified by the known wave qualities of electromagnetic radiation. Quantum Electrodynamics also uses spreading wave amplitudes; not flying particles. The evidence indicates that light is a wave and electrons are electromagnetic wave-structures that absorb and emit light in discrete wave-packets. These wave-quanta are emitted directionally and then spread in space in proportion to their wavelength. Their waves superposition with all other waves in space. In low intensity experiments, the waves that an electron in a photodetector absorbs come from the superpositioning of the source wave-quanta and background radiation. The importance of background radiation is evidenced by "dark counts". Treating electrons and the quanta they absorb and emit as particles when they are composed of waves is the source of all the paradoxes, unreality and confusion in Quantum Mechanics. The word "photon" should be replaced by "quantum" in the description of this particular electronic process. The conceptual model presented here explains the known phenomena without producing paradoxes and unifies quantum and classical electromagnetics.
In isolated-core excited Rydberg systems the destruction of quantum coherence by spontaneous emission of photons is investigated. For this purpose a theoretical description is developed which is based on a decomposition of the atomic density operator into N-photon contributions. Using methods from multichannel quantum defect theory, the relevant atomic transition amplitudes are represented in the form of semiclassical path representations which are associated with repeated returns of the Rydberg electron to the ionic core. Apart from numerical advantages, this approach also yields a clear physical picture of the intricate interplay between the incoherent photon emission process, the coherent laser-modified electron correlation effects, and the semiclassical aspects of the dynamics of the Rydberg electron. Various examples of this interplay are analyzed within the framework of the developed theoretical tools. \textcopyright{} 1996 The American Physical Society.