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European Journal of Physics

Matter wave propagation using the Fourier optics approach

Mahdi Shayganmanesh, Ayoob Hematizadeh

Published Aug 10, 2016• 1 citation
Publisher

Abstract

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.

DOI
10.1088/0143-0807/37/5/055304

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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 Basic explanations of the double slit diffraction phenomenon include a description of waves that emanate from two slits and interfere. The locations of the interference minima and maxima are determined by the phase difference of the waves. An optical wave, which has a wavelength and propagates a distance accumulates a phase of A matter wave, also having wavelength that propagates the same distance accumulates a phase of which is a factor of two different from the optical case. Nevertheless, in most situations, the phase difference, for interfering matter waves that propagate distances that differ by is approximately which is the same value computed in the optical case. The difference between the matter and optical case hinders conceptual explanations of diffraction from two slits based on the matter–optics analogy. In the following article we provide a path integral description for matter waves with a focus on conceptual explanation. A thought experiment is provided to illustrate the validity range of the approximation .
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.
Motion of microscopic particles has been a very interesting topic.In order to explain the matter wave diffraction problem better,this paper using the new method of quantum theory to studies the Double-slit diffraction of C60 molecules using the new method of quantum theory.First,solve the Double slit diffraction of C60molecules wave functions by Schrodinger equation.Then calculate the diffraction wave function after the slit of C60 molecules with the Feynman path integral quantum theory.To obtain diffraction wave function of diffraction screen.Finally the analytic relation between the double-slit relative diffraction intensity and diffraction pattern position of C60molecules is obtained.The calculation results are in good agreement with the experimental data.This shows that the diffraction microscopic particles need to be studied with quantum theory method completely.This method has universality for the study of the motion of microscopic particles.It also can be used in the study of single slit diffraction, Multi-slit diffraction and grating diffraction for matter wave and other particles.
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.