Nonlocal advection diffusion equations and the two-slit experiment in quantum mechanics

IF 0.8 4区数学 Q2 MATHEMATICS

Electronic Journal of Differential Equations Pub Date : 2023-03-27 DOI:10.58997/ejde.sp.02.w1

Glenn Webb

引用次数: 0

Abstract

We analyze a partial differential equation that models the two-slit experiment of quantum mechanics. The state variable of the equation is the probability density function of particle positions. The equation has a diffusion term corresponding to the random movement of particles, and a nonlocal advection term corresponding to the movement of particles in the transverse directionperpendicular to their forward movement. The model is compared to the Schrodinger equation model of the experiment. The model supports the ensemble interpretation of quantum mechanics. See also https://ejde.math.txstate.edu/special/02/w1/abstr.html

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量子力学中的非局部平流扩散方程与双缝实验

我们分析了一个模拟量子力学双缝实验的偏微分方程。方程的状态变量是粒子位置的概率密度函数。方程有一个扩散项对应于粒子的随机运动，一个非局部平流项对应于粒子在垂直于它们的向前运动的横向运动。将该模型与实验中的薛定谔方程模型进行了比较。该模型支持量子力学的系综解释。参见https://ejde.math.txstate.edu/special/02/w1/abstr.html

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Electronic Journal of Differential Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.50

自引率

14.30%

发文量

审稿时长

3 months

期刊介绍： All topics on differential equations and their applications (ODEs, PDEs, integral equations, delay equations, functional differential equations, etc.) will be considered for publication in Electronic Journal of Differential Equations.