# The nonlocal advection diffusion equation and the two-slit experiment in quantum mechanics

**Authors:** Glenn Webb  
**arXiv:** [2303.10061](https://arxiv.org/abs/2303.10061)  
**Date:** 2023-03-17  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2303.10061v1/

## Key points

- Partial differential equation model for the two-slit experiment in quantum mechanics
- State variable: probability density function of particle positions
- Equation includes diffusion term and nonlocal advection term
- Comparison with Schrödinger equation model
- Aim to provide insights into particle behavior in quantum mechanics
- Analysis supports ensemble interpretation of quantum mechanics and experimental observations
- Ensemble interpretation explains interference patterns observed in double-slit experiments
- Numerical simulations conducted for both models to validate predictions and compare results
- Simulations aid in visualizing particle behavior and understanding quantum mechanics at a microscopic level
- Alternative mathematical model for analyzing the two-slit experiment
- Supports existing theories while offering new insights into particle behavior

## Summary

This paper analyzes a partial differential equation model for the two-slit experiment in quantum mechanics. The state variable of the equation is the probability density function of particle positions. The equation includes a diffusion term and a nonlocal advection term to account for random and transverse movements of particles. The model is compared to the more commonly known Schrödinger equation model. Through this comparison, the author aims to provide further insights into particle behavior in quantum mechanics. The analysis supports the ensemble interpretation of quantum mechanics and its alignment with experimental observations. This interpretation offers a framework for understanding phenomena such as interference patterns observed in double-slit experiments. Additionally, numerical simulations are conducted for both models to validate their predictions and compare results. These simulations aid in visualizing particle behavior in different scenarios and contribute to our understanding of quantum mechanics at a microscopic level. Overall, this study provides an alternative mathematical model for analyzing the two-slit experiment and supports existing theories while offering new insights into particle behavior.