https://interactive-quantum-monte-carlo.onrender.com/

This project simulates the interference pattern observed in a double slit experiment using the Monte Carlo method. The simulation is implemented in Python and provides an interactive visualization using Plotly and Dash.

The double slit experiment demonstrates the wave-particle duality of particles such as electrons. When particles pass through two slits, they create an interference pattern on a screen, characteristic of wave behavior. This project aims to numerically simulate this interference pattern using the Monte Carlo method.

The goal is to simulate the interference pattern produced by a double slit experiment. Traditional analytical methods are complex and limited in handling large-scale simulations. A numerical approach using the Monte Carlo method provides a flexible and scalable solution.

The Monte Carlo method is a statistical technique that uses random sampling to solve numerical problems. It is suitable for this simulation because:

•	It efficiently handles a large number of particles.
•	Its stochastic nature mimics the randomness observed in quantum experiments.
•	It is flexible and can be adapted to different scenarios and complexities.

The function calculates the probability distribution of particle positions using the interference pattern formula:

$P(x) \propto \left( \cos \left( \frac{\pi d x}{\lambda l} \right) \right)^2 $

Monte Carlo Simulation

•	Random Sampling: Generate random x positions for particles passing through the slits.
•	Probability Calculation: Use the diffraction function to calculate the probability of each position.
•	Acceptance-Rejection: Accept or reject positions based on calculated probabilities to simulate the actual distribution on the screen.

The project uses Plotly and Dash to create interactive plots for real-time parameter adjustments and visualization. The outputs include:

•	Scatter Plot: Displays individual particle positions.
•	Histogram: Shows the distribution of particle positions.
•	Theoretical Model Overlay: Compares simulated data with theoretical predictions.