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College Physics

The matter wave explanation of single slit diffraction

LI Wu-jun

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

The photon's single slit diffraction is explained from matter wave of quantum mechanics, the same conclusion with Huygens-Fresenel principle is concluded. This method could help students to understand wave function concept and statistical meaning of quantum mechanics.

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Journal of Yulin University•Jan 1, 2006•0 citations

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Dynamical Origin of Single‐Slit Diffraction From Single‐Photon Momentum Recoil and Velocity‐Perpendicular Particle‐Wave Interaction

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ABSTRACT In this study, we propose a formula to characterize the mechanical properties of microscopic particles from the particle‐wave interaction perspective, defining the corresponding interaction as a velocity‐perpendicular interaction force. Traditional single‐slit diffraction is mainly explained by wave theory and the Huygens–Fresnel principle. However, the single‐photon momentum recoil in diffraction suggests that it is feasible to decouple the particle and wave natures of both photons and the slit, thereby exploring the interaction force between them in depth. We find that photons at different positions inside the slit experience velocity‐perpendicular interaction force, leading to net interaction time differences related to their distances to the slit edges. Based on wave‐particle duality, the modulation quantity formed by the interaction force, net interaction time, slit scale, and Planck constant exerts an on‐off modulation effect. Within this model, photons form clear diffraction fringes, which are rigorously verified to be fully consistent with the Huygens–Fresnel principle. This work provides a dynamical reinterpretation of single‐slit diffraction and establishes a mechanical framework for quantitatively describing quantum phenomena involving particle‐wave interaction.

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A quantum-mathematical model to state single photon (electron) double slit experiment, Fraunhofer and Fresnel diffractions

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This paper provides a complete physical model associated with mathematical analysis and formulation that is based on Schrödinger equation and Feynman path integral. This model answers to single Photon (electron) double slit experiment with high degree of accuracy. It also gives a new method of analysis and formulation for Fresnel and Fraunhofer diffractions that are completely according to the Schrödinger equation and Feynman path concept. The results of these methods are precisely in agreement with the near field and far field diffraction experiments. In other words the new formulation in all above mentioned phenomena i.e. single photon (electron) double slit experiment, Fresnel and Fraunhofer diffractions are completely confirmed by lab experiments(measurements). Lab experiments mean common intensity and pattern experiments resulting from Fresnel (near field) diffraction, Fraunhofer (far field) diffraction and patterns resulting in single photon (electron) lab experiment. The resultant formulas are sketched and calculated by matlab program, the resultant graphs and values are compared with lab experiments in each section. This analysis substitutes wave function and probability density function concepts instead of interference of light beams emitted from infinitesimal pinholes or classical interpretation of near field diffraction and far field diffraction phenomena. The ultimate goal of this paper is to give a very accurate answer to the single particle double slit experiment and also to unify diffraction concept of classical optics in to quantum mechanics, deleting the traditional concept of phases in classical optics and substituting the concept of deflection of Feynman paths. The above mentioned analysis may be a glad tiding to a reliable method to unify classical optics in to quantum mechanics.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 26, 2007•0 citations
The characteristic of light is the wave and particle.From the perspective of probability wave in quantum mechanics,the thesis describes the wave function of microcosmic particle and derives the distributive law of light intensity of the single slit and multiple-slit fraunhofer diffraction by means of the probability wave.The result accords with that obtained through the Huygens-Fresnel Principle.This method could help students to understand the wave function concept and the statistical meaning of wave function in quantum mechanics and understand the essence of light.
Abstract In this paper propagation of matter wave of particles is modeled using the Fourier optics approach. In first step the Schrödinger equation of quantum mechanics is used to find the wave function of the particle. In the second step Fourier optics is employed to model the diffraction of the wave function of the particle through single and double slits. The results of the calculations are presented as graphs of diffraction patterns. The results of the presented method are compared to the existing results in the literature (with different methods) to check the validity of the introduced model. It is shown that the Fourier optics approach is applicable to matter wave of particles in diffraction through slits.
Abstract In Chapter 21, we turn to interference and diffraction. We start by describing the interference pattern in Young’s classic two-slit experiment, whose analysis is subsequently generalised to determine the interference pattern behind a multi-slit grating. The diffraction pattern for a single slit is then estimated using Huygens’ principle, and this is combined with the interference pattern for a multi-slit grating to get the entire wave pattern generated by a diffraction grating. Next, we turn to the diffraction of electrons. This starts with a brief introduction to quantum mechanics, focussed on Schrodinger’s wave equation, de Broglie waves, and the collapse of the wavefunction following measurements. Finally, we use these elementary quantum concepts to describe the diffraction of electrons.
ABSTRACT In this study, we propose a formula to characterize the mechanical properties of microscopic particles from the particle‐wave interaction perspective, defining the corresponding interaction as a velocity‐perpendicular interaction force. Traditional single‐slit diffraction is mainly explained by wave theory and the Huygens–Fresnel principle. However, the single‐photon momentum recoil in diffraction suggests that it is feasible to decouple the particle and wave natures of both photons and the slit, thereby exploring the interaction force between them in depth. We find that photons at different positions inside the slit experience velocity‐perpendicular interaction force, leading to net interaction time differences related to their distances to the slit edges. Based on wave‐particle duality, the modulation quantity formed by the interaction force, net interaction time, slit scale, and Planck constant exerts an on‐off modulation effect. Within this model, photons form clear diffraction fringes, which are rigorously verified to be fully consistent with the Huygens–Fresnel principle. This work provides a dynamical reinterpretation of single‐slit diffraction and establishes a mechanical framework for quantitatively describing quantum phenomena involving particle‐wave interaction.
This paper provides a complete physical model associated with mathematical analysis and formulation that is based on Schrödinger equation and Feynman path integral. This model answers to single Photon (electron) double slit experiment with high degree of accuracy. It also gives a new method of analysis and formulation for Fresnel and Fraunhofer diffractions that are completely according to the Schrödinger equation and Feynman path concept. The results of these methods are precisely in agreement with the near field and far field diffraction experiments. In other words the new formulation in all above mentioned phenomena i.e. single photon (electron) double slit experiment, Fresnel and Fraunhofer diffractions are completely confirmed by lab experiments(measurements). Lab experiments mean common intensity and pattern experiments resulting from Fresnel (near field) diffraction, Fraunhofer (far field) diffraction and patterns resulting in single photon (electron) lab experiment. The resultant formulas are sketched and calculated by matlab program, the resultant graphs and values are compared with lab experiments in each section. This analysis substitutes wave function and probability density function concepts instead of interference of light beams emitted from infinitesimal pinholes or classical interpretation of near field diffraction and far field diffraction phenomena. The ultimate goal of this paper is to give a very accurate answer to the single particle double slit experiment and also to unify diffraction concept of classical optics in to quantum mechanics, deleting the traditional concept of phases in classical optics and substituting the concept of deflection of Feynman paths. The above mentioned analysis may be a glad tiding to a reliable method to unify classical optics in to quantum mechanics.