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Single-Slit Diffraction

The Physics​

When a wave passes through a narrow opening, it diffracts - spreading out in a characteristic pattern. This is a fundamental property of waves, whether they're water waves, sound waves, or quantum probability waves.

The single-slit diffraction pattern shows:

  • A central maximum directly behind the slit
  • Secondary maxima of decreasing intensity on either side
  • Dark minima where destructive interference occurs

The Diffraction Equation​

The angular positions of the dark fringes follow: a sin(θ) = nλ (n = 1, 2, 3, ...)

Where:

  • a is the slit width
  • θ is the angle from the central axis
  • λ is the wavelength
  • n is the order of the minimum

What You'll See​

1. Initial State​

A Gaussian wavepacket approaches the barrier from the left. The wavepacket has a well-defined momentum (direction of travel) but is localized in space.

2. Interaction with Slit​

When the wavepacket reaches the barrier, most of it is reflected. Only the portion passing through the slit continues.

3. Diffraction Pattern Emerges​

After passing through, the wave spreads out. The probability density forms the characteristic single-slit pattern with a bright central band.

4. Far-Field Pattern​

At the detector (right side of simulation), we see the intensity pattern - brightest at center, falling off with characteristic oscillations.

The Simulation​

Grid: 512 × 512 points
Slit width: 8.0 units
Barrier height: 1000 (effectively infinite)
Wavepacket momentum: kx = 3.0

Animation​

The video above shows the wavepacket evolution in real-time, demonstrating how the probability density evolves as the quantum particle passes through the slit.

Run It Yourself​

claude -p "Simulate single-slit diffraction: Create a barrier at x=85 with one slit \
  (height=15), use an elliptical wavepacket with width=[15,50] (vertical long axis), \
  show potential overlay, add sensor line at x=220, and save to /tmp/single_slit.gif" \
  --allowedTools "mcp__quantum-mcp__*"

Key Observations​

  1. Wave Nature: The spreading after the slit proves the wave nature of the quantum particle
  2. Uncertainty Principle: Confining the particle's position (narrow slit) spreads its momentum (diffraction)
  3. Intensity Distribution: Follows the sinc² function: I(θ) ∝ (sin(β)/β)² where β = πa sin(θ)/λ