Time Evolution of a Quantum Wave Packet in a 1D Box

This project simulates the time evolution of a quantum particle in a 1D infinite potential well using the Crank–Nicolson method. The simulation visualizes the probability density, real part, and imaginary part of the wavefunction through 2D/3D plots and animations.

I have designed the simulation inspired by Adib Kabir's Numerical Simulation of the Time-Dependent Schrödinger Equation Using the Crank-Nicolson Method

Python libraries used: NumPy, SciPy, and Matplotlib

Features

• Numerical solution of the time-dependent Schrödinger equation (TDSE).
• Implementation of the Crank–Nicolson scheme with sparse matrices for efficiency.
• Multiple visualization modes:
  • 2D plots at single or multiple timesteps.
  • 3D plots of the wavefunction.
  • 2D and 3D animations of the wave packet evolution.
  • Option to save animations as .mp4 files (requires ffmpeg).

Requirements

Ensure you have the following Python packages installed :

python -m pip install numpy matplotlib scipy

Additionally, ffmpeg is required if you want to save animations as videos.

How to Run

Clone the repository:

git clone https://github.com/Shashi0969/Crank-Nicolson-Algorithm.git
cd Crank-Nicolson-Algorithm

Run the script:

Particle_in_a_1D_box.py

You will be prompted with options:

Enter '1' to start and '0' to terminate :

If you enter 1, you can choose:

1. 2D plot at 2000th step
2. 3D plot at 2000th step
3. 2D plots at 500th, 1000th, 1500th, and 2000th steps
4. 3D plots at 500th, 1000th, 1500th, and 2000th steps
5. 2D animation of evolution
6. 3D animation of evolution

Outputs:

2D Plot: Probability density, real and imaginary parts at a specific timestep.

3D Plot: Real vs imaginary part evolution in 3D space.

Animation: Continuous time evolution of the wavefunction.

Notes

• Default parameters simulate an electron in a 1D box of length $10^{-8}$ m.
• You can modify wave packet parameters (sigma, $k_0$, etc.) in the Start() function.