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Journal of Yulin University

Interpretation of Light Diffraction from the Perspective of Matter Wave

Yu Jian

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

Light has the quality of wave and particle. From the perspective of matter wave in quantum mechanics, this paper, by describing the wave function of microcosmic particle and using probability wave, derives the distributive regularity of light intensity of the single slit diffraction and circular aperture diffraction. The result is in line with the Huygens - Fresnel Principle.

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Light has the quality of wave and particle. From the perspective of matter wave in quantum mechanics, this paper, by describing the wave function of microcosmic particle and using probability wave, derives the distributive regularity of light intensity of the single slit diffraction and circular aperture diffraction. The result is in line with the Huygens - Fresnel Principle.
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.
Using the Fresnel–Kirchhoff integral, we express the state of the light that diffracts from an aperture to a point, by superposition of two or more waves. The amplitudes of the waves are determined by the distances of the point from the ray optics borders of the emerging beams. The interference approach to the Fresnel diffraction leads to a universal formulation of the normalized intensity distribution on the diffraction pattern that determines the state of the incident light, the parameters of the aperture, and its distance from the observation plane, uniquely. In the photon approach, according to the uncertainty principle, confining the position of a photon to an aperture changes the probable propagation direction of the photon in an interval that leads to the diffraction of the photon or light. Thus, the normalized intensity distribution on the diffraction pattern is the probability distribution of a photon. To this probability distribution, a probability amplitude distribution is associated that diffracts similar to a wave in Fresnel diffraction. Applying the introduced approach to the study of the diffraction, from different simple apertures and phase steps, we deduce general behaviors of the Fresnel diffraction and show it is involved in all aspects of light phenomena.
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.
In this paper, we discuss some light diffraction phenomena with a simple quantum theory. Firstly, the wave function of the free particle in quantum mechanics is used to explain Fraunhofer diffraction of the light at a rectangular aperture, and the result is consistent with the Huygens-Fresnel principle. Secondly, probabilistic wave method is used to analyze the Talbot effect of a two-dimensional grating. The results show that the photons at the Talbot distance and incident photons are described by the same probability wave. Finally, Talbot effect is used to measure the wavelength of incident light.