Visual Demonstrations
Dramatic visualizations showcasing the computational physics capabilities of the Math MCP ecosystem.
These demos demonstrate:
- Quantum mechanics simulations using the Schrödinger equation
- Molecular dynamics with N-body gravitational interactions
- Language models training and text generation
- Real-time visualization and video rendering
Quantum Mechanics Demos
Slit Diffraction Series
Experience the most famous experiments in quantum mechanics - wave interference through single, double, and triple slits.
| Demo | Description |
|---|---|
| Single-Slit Diffraction | Classic diffraction pattern from a single narrow opening |
| Double-Slit Interference | The quintessential quantum experiment showing wave-particle duality |
| Triple-Slit Interference | Complex interference patterns from three coherent sources |
Bragg Scattering Series
Watch quantum wavepackets scatter from crystal lattice structures, revealing the atomic arrangement through diffraction patterns.
| Demo | Description |
|---|---|
| Square Lattice | Scattering from a simple cubic-like crystal structure |
| Hexagonal Lattice | Graphene-like honeycomb atomic arrangement |
Molecular Dynamics Demos
Galaxy Collision
Spectacular N-body gravitational simulation of colliding galaxies.
| Demo | Description |
|---|---|
| Galaxy Collision | Two spiral galaxies merge, creating tidal tails and bridges |
Language Model Demos
LLM Training
Train language models from scratch using GPT and Mamba architectures.
| Demo | Description |
|---|---|
| GPT Training | Train a GPT model on text and generate stories |
Running the Demos
Run demos interactively with Claude Code:
claude -p "Simulate double-slit interference and save to /tmp/demo.gif" \
--allowedTools "mcp__quantum-mcp__*"
Or start an interactive session:
cd /path/to/math-mcp
claude
# Then ask: "Simulate a galaxy collision"
The Physics Behind the Demos
Quantum Simulations
All quantum demos use the split-step Fourier method to solve the time-dependent Schrödinger equation. The algorithm alternates between:
- Position space: Apply potential energy operator
- Momentum space: Apply kinetic energy operator (via FFT)
This preserves unitarity and handles both bound and scattering states.
Molecular Dynamics
The galaxy collision uses Velocity Verlet integration with gravitational softening. The softening parameter prevents numerical instabilities when particles pass close together.