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Journal of Yichun College

The Probability Wave Analysis of Single-slit and Multiple-slit Diffraction of Light

Jianli Yu

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

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.

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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.
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.
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.
In this paper,the light double-slit diffraction with quantum theory approach is studied.Firstly,the light wave function in slits is calculated,and the diffraction wave function is obtained with Kirchhoff’s law.The diffraction intensity is proportional to the diffraction wave function da party.Futhermore,the intensity formula of light double-slit diffraction is obtained;by comparing the quantum theory calculation results and classical electromagnetic theory calculation results and the experimental date,it is found that the calculate result of quantum theory is in accordance with the experment data,but the classical electromagnetic theory calculation result with the experiment date has certain deviation.So,the quantum theory can explain the light diffraction more precisely.The proposed method can also further study the light of the single slit,many slits and grating diffraction experiment phenomena.