# Triple-Slit Interference Demo
## The Prompt
```
Now show me triple-slit interference. Three slits should create a more
complex pattern with subsidiary maxima. Compare it to the double-slit case.
```
## MCP Tool Sequence
### Step 1: Create Triple-Slit Potential
```tool
mcp__quantum-mcp__create_custom_potential
grid_size: [256, 256]
function: "1000 * ((np.abs(x - 128) < 3) & (np.abs(y - 98) > 5) & (np.abs(y - 128) > 5) & (np.abs(y - 158) > 5))"
```
Three slits at y = 98, 128, 158 (equal spacing of 30 units).
### Step 2: Wide Coherent Wavepacket
```tool
mcp__quantum-mcp__create_gaussian_wavepacket
grid_size: [256, 256]
position: [40, 128]
momentum: [2.5, 0]
width: 30
```
### Step 3: Simulate
```tool
mcp__quantum-mcp__solve_schrodinger_2d
potential: "potential://triple-slit"
initial_state: <wavefunction>
time_steps: 600
dt: 0.02
```
### Step 4: Render
```tool
mcp__quantum-mcp__render_video
simulation_id: "simulation://triple-slit"
output_path: "/tmp/triple_slit.mp4"
fps: 30
```
## Expected Results
### Pattern Structure
```
Double-Slit: Triple-Slit:
██ ██ ██ ████ ██ ████ ██ ████
↑ ↑
subsidiary subsidiary
maxima maxima
```
Key differences:
- **Sharper principal maxima** (narrower peaks)
- **Subsidiary maxima** appear between main peaks
- **More complex structure** from 3-wave interference
### Intensity Formula
For N slits:
$$I(\theta) = I_0 \left(\frac{\sin(N\beta/2)}{\sin(\beta/2)}\right)^2$$
where $\beta = \frac{2\pi d \sin\theta}{\lambda}$
For N=3: Principal maxima with 1 subsidiary maximum between each pair.
## Comparison Prompt
```
Create a side-by-side comparison showing single, double, and triple slit
interference patterns from the same incoming wavepacket.
For each case, extract the intensity pattern at a detector screen position
x = 200 and plot them together.
```
### Expected Comparison Tool Calls
1. Run all three simulations
2. Use `analyze_wavefunction` on final states
3. Extract 1D slices at detector position
4. Compare the patterns
## Toward Diffraction Gratings
```
What happens with 5 slits? 10 slits? Show me how the pattern evolves
as we approach a diffraction grating with many slits.
```
As N increases:
- Principal maxima become **sharper** (width ~ 1/N)
- More subsidiary maxima appear (N-2 between each pair)
- Approaches delta-function peaks of ideal grating
