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Journal of Tianjin University Science and Technology

Quantitative Analysis for Matter-Wave Multiple-Slit Interference Effect

Zhou Pei

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

The interference effect caused by plane electron probability wave through N (≥2) slits is taken for the examples. Feynman′s path integral theory is used to analyse quantitatively the electronic multiple slit interference state .The electron wave intensity space distribution function obtained is totally the same as that of light wave multiple slit interference. The method is simple, convenient and can be directly perceived through the senses.

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The interference effect caused by plane electron probability wave through N (≥2) slits is taken for the examples. Feynman′s path integral theory is used to analyse quantitatively the electronic multiple slit interference state .The electron wave intensity space distribution function obtained is totally the same as that of light wave multiple slit interference. The method is simple, convenient and can be directly perceived through the senses.
In this article we hold on an analytic solution of the well-known cases of difraction and interference of electrons through one and two slits (simply that, the one-dimensional case is assumed only). In addition, we hold an approximations of the electron distribution which offer the interpretation of the results. Our derivation is based on the Feynman path integral formula and this work could also serve an awesome introduction to multiple slits interference. Then it is comparing between theoretical results and simulation in order to get interference pattern of it.
Superposition principle of wave function in multi-slit interference experiment has been widely accepted by many quantum mechanics textbooks, however the expression ψAB=ψA+ψB{ψ_{AB}} = {ψ_A} + {ψ_B}ψAB​=ψA​+ψB​ does not strictly hold. The non-classical paths in Feynman path integral provide an explanation to the multi-path interference effect, and can be used to quantitatively analyse the multi-slit interference effect. In this work, we apply quantities in Bohmian mechanics to the measurement of multi-order interference by analysing the contribution of non-classical paths to Bohmian velocity in electron's multi-slit interferometer. The result shows that the non-classical paths effect will cause a relative deviation of 10−310^{-3}10−3 in electron's Bohmian velocity, which is observable by doing weak measurement similar to previous work.
Aim To quantitatively analyze and explain the A-B effect,and potential A has the physical effect which may been observed.Methods Feynman's path integral and quantum theory are used to analyze quantitatively phase shift of electron probability wave resulting from the magnetic vector-potential A and then the A-B effect is explained.Results Although the electronic movement goes to region without any action to exert on the electronic,some extra factor attaches actually in the electronic probability wave,and appears the interference fringe movement through the quantum interference,but moves to position through the zero order enormous stripe,may measure in the circular solenoid magnetic .Conclusion The local field effect B is not used to describe A-B effect,but phase factor is that can completely appropriate description magnetic field physical quantity.
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.