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

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  • Ezzat G. Bakhoum
  • Cristian Toma

Abstract

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.

Suggested Citation

  • Ezzat G. Bakhoum & Cristian Toma, 2015. "Alternating Coordinate-Momentum Representation for Quantum States Based on Bopp Operators for Modelling Long-Distance Coherence Aspects," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-7, April.
    • Handle: RePEc:hin:jnlmpe:818019
    DOI: 10.1155/2015/818019
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