Quantum phenomena in numerical wave propagation
作者:
Robert Vichnevetsky,
期刊:
International Journal for Numerical Methods in Fluids
(WILEY Available online 1989)
卷期:
Volume 9,
issue 6
页码: 623-650
ISSN:0271-2091
年代: 1989
DOI:10.1002/fld.1650090602
出版商: John Wiley&Sons, Ltd
关键词: Numerical analysis;Wave propagation;Hyperbolic equations;Quantum mechanics
数据来源: WILEY
摘要:
AbstractThe analysis of wave propagation in computing domains where hyperbolic equations are approximated with finite differences has revealed surprising analogies between this subject and quantum mechanics. The first part of this paper consists of a review of the corresponding phenomena and of their description with known results from numerical analysis and wave propagation theory. We then introduce a new formalism, containing a finite difference analogue of the classical Schrodinger equation, which describes the ensemble of those phenomena. The validity of the new formalism is verified by its agreement with known theoretical results in numerical wave propagation (it contains in fact many of those results) as well as with new data obtained in numerical experiments with monochromatic waves which display properties similar to those of Schrödinger's wavefunction for the quantum mechanics description of the equivalent experiments with physical particles. While the results of this paper are derived in the context of wave propagation in computing domains, they remain applicable to similar aspects of wave propagation in other (physical) periodic structures
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