This project simulates and visualizes quantum mechanical wavefunctions for a particle in a 1D and 2D infinite potential well (particle in a box) using Python, NumPy, Pandas, Matplotlib, and Seaborn. It generates probability densities, energy levels, and interactive visualizations to deepen understanding of quantum phenomena.
✅ Plots 1D wavefunctions ψₙ(x) for quantum numbers n=1 to 5
✅ Plots probability densities |ψₙ(x)|² in 1D
✅ Overlays classical vs quantum probability densities
✅ Visualizes discrete quantum energy levels Eₙ
✅ Generates 2D probability density heatmaps for ψₙₘ(x,y) in a 2D box
✅ Written in a clean, well-commented Jupyter Notebook
✅ Saves plots as images for documentation
The particle in a box is a fundamental solution to the time-independent Schrödinger equation. For a box of length L:
- The 1D wavefunction solutions are: [ \psi_n(x) = \sqrt{\frac{2}{L}} \sin\left(\frac{n\pi x}{L}\right), \quad n=1,2,3,... ]
- The 2D wavefunction solutions are: [ \psi_{n,m}(x, y) = \frac{2}{L} \sin\left(\frac{n \pi x}{L}\right) \sin\left(\frac{m \pi y}{L}\right) ]
Probability density |ψ|² gives the probability of finding the particle at a given location.
- Python 3.x
- Jupyter Notebook
- NumPy
- Pandas
- Matplotlib
- Seaborn
- Clone the repository:
git clone https://github.com/your-username/quantum-wavefunction-visualizer.git cd quantum-wavefunction-visualizer