This repository collects small Python projects and a final course project demonstrating physics concepts through simulation and visualization.

• Visualizes constructive/destructive interference from pairs of sinusoids.
• Emphasizes how frequency, phase, and amplitude shape the resulting waveform.
• Includes example plots/animations for fast visual inspection of effects.

• Simulates a 2D idealized gas with elastic particle–particle and particle–wall collisions.
• Tracks trajectories, speeds, and aggregate statistics; illustrates approach to equilibrium.
• Useful for discussing conservation laws and links to Maxwell–Boltzmann intuition.

• Report: Numerical_Optics.pdf
• Implements multiple solvers for the paraxial wave/propagation equation:
  • Rayleigh–Sommerfeld integral, Leapfrog FD, Forward Euler, and Crank–Nicolson.
• Compares stability, boundary conditions, and computational trade-offs; includes derivations and results.

• Notebook: Anharmonic_Oscillator.ipynb
• Derives equations of motion (Lagrangian → Hamiltonian → nonlinear ODE) and analyzes:
  • Amplitude-dependent period (elliptic integral), parametric driving, inverted-pendulum stabilization,
  • Onset of chaos and sensitivity to initial conditions (with RK4 simulations and phase portraits).

• Report: Laplace_Relaxation.pdf
• Implements a 2D relaxation solver on a rectangular grid and benchmarks against an analytic Fourier-series solution.
• Includes convergence checks, error metrics (RMSE/percent accuracy), and side-by-side visual comparisons.

The scripts require Python 3.x and the following external libraries:

• NumPy
• Matplotlib
• SciPy

You can install them with:

pip install numpy matplotlib scipy

Clone the repo and run any script:

git clone https://github.com/hschn58/Physics.git
cd Physics/Wave_Superposition
python3 wave_superposition.py

Wave Superposition	Particle Dynamics	Rayleigh–Sommerfeld Integral

This project is licensed under the MIT License.