Quantum phenomena in numerical wave propagation

The 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 descri...

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Veröffentlicht in:International journal for numerical methods in fluids 1989-06, Vol.9 (6), p.623-650
1. Verfasser: Vichnevetsky, Robert
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description The 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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subjects Exact sciences and technology
finite difference method
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Hydrodynamic waves
Hyperbolic equations
Numerical analysis
Physics
Quantum mechanics
Wave propagation
title Quantum phenomena in numerical wave propagation
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