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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 818019, 7 pages
Research Article

Alternating Coordinate-Momentum Representation for Quantum States Based on Bopp Operators for Modelling Long-Distance Coherence Aspects

1Department of Electrical and Computer Engineering, University of West Florida, 11000 University Parkway, Pensacola, FL 32514, USA
2Faculty of Applied Sciences, Politehnica University, 315 Splaiul Independentei, 060042 Bucharest, Romania

Received 6 August 2014; Accepted 22 August 2014

Academic Editor: Florin Pop

Copyright © 2015 Ezzat G. Bakhoum and Cristian Toma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This study presents an alternating coordinate-momentum representation for propagation and transition of associated wave function, based on Bopp operators and on a certain symbolic determinant corresponding to a set of two linear equations with null free terms. It is shown that this alternating representation can justify in a good manner the patterns created through reflection/refraction of waves on nonperfectly smooth interfaces and phase correspondence of diffracted beams without the need of supplementary support functions. Correlations with Lorentz transformation of wave functions by interaction with a certain material medium (the space-time origin of a wave-train being adjusted) are also presented, and supplementary aspects regarding the use of electromagnetic scalar and vector potentials for modelling evolution within this alternating representation are added.