matlab simulation of the atom in graphly way 🔬 Heisenberg Uncertainty Principle Simulation (MATLAB)
A high-precision MATLAB simulation demonstrating the Heisenberg Uncertainty Principle through Gaussian wave packets, Fourier transforms, and quantum wave packet evolution.
This project numerically and visually verifies:
Δ 𝑥 ⋅ Δ 𝑝 ≥ ℏ 2 Δx⋅Δp≥ 2 ℏ
and shows how narrowing position uncertainty increases momentum uncertainty — a fundamental concept of quantum mechanics.
🚀 Features 📌 1. Gaussian Wave Packet Modeling
Normalized quantum wave function in position space
Adjustable position spread (σₓ)
Central wave number control
📌 2. Position ↔ Momentum Duality
Numerical Fourier Transform (FFT)
Momentum-space probability density
Proper normalization in both domains
📌 3. Uncertainty Verification
Computes Δx and Δp
Displays uncertainty product
Demonstrates minimum uncertainty condition
📌 4. Trade-off Curve Visualization
Plots theoretical boundary:
ℏ 2 Δ 𝑥 Δp= 2Δx ℏ
Highlights allowed and forbidden regions
Marks simulation test cases
📌 5. Time Evolution Animation
Free-particle wave packet dispersion
Group velocity implementation
Time-dependent spreading:
𝜎 𝑥 1 + ( ℏ 𝑡 2 𝑚 𝜎 𝑥 2 ) 2 σ(t)=σ x
1+( 2mσ x 2
ℏt
) 2
🧠 Concepts Applied
Quantum Mechanics
Fourier Analysis
Gaussian Wave Packets
Numerical Simulation
Scientific Visualization
MATLAB Graphics & Animation
🛠 Built With
MATLAB
FFT algorithms
Custom frequency grid implementation
Dynamic plotting & animation tools
📊 Output
Side-by-side position & momentum distributions
Heisenberg boundary curve
Animated wave packet spreading
Research-style scientific visualizations
🎯 Purpose
This project demonstrates strong skills in:
Computational physics
Mathematical modeling
Numerical methods
Scientific programming in MATLAB
LINKEDIN ID :https://www.linkedin.com/in/rishi-gupta-85bab0232/ ABOUT ME : https://rishiguptainfo.vercel.app/