Heisenberg Wavepacket & Uncertainty Simulator

Spatial Width (Δx) 1.500 a.u. Position uncertainty

Momentum Spread (Δp) 0.333 a.u. Fourier conjugate uncertainty

Uncertainty Product 0.500 ħ ✓ Minimum Uncertainty State

Fourier Components 64 waves Superposition count

Real-Space Wavefunction Ψ(x, t)

Drag center x₀ or Δx slider

Cyan: Re(Ψ) | Magenta: Im(Ψ) | Amber Area: |Ψ|²

Momentum-Space Spectrum Φ(p)

Fourier Transform Distribution

Amber Curve: |Φ(p)|² Momentum Probability

Wavepacket Parameters Real-time Fourier Synthesis

Spatial Uncertainty (Δx) 1.50

Central Momentum (p₀) 2.00

Center Position (x₀) 0.00

Potential Barrier Height (V₀) 0.00

Physical Scenarios

📖 Quantum Philosophy & Mathematical Foundation

In Physics and Philosophy (1958), Werner Heisenberg explained that quantum mechanics fundamentally changed our view of objective reality. The Uncertainty Principle is not merely a limitation of experimental apparatus—it is an intrinsic property of wave-particle duality.

Δx · Δp ≥ ħ / 2 | Ψ(x) = (1 / (2π Δx²)^(1/4)) · exp(-(x - x₀)² / (4 Δx²)) · exp(i p₀ x / ħ)

When you compress the spatial footprint Δx of a wavepacket, its constituent momentum Fourier spectrum Φ(p) spreads out proportionally. Clicking Simulate Measurement collapses the probability distribution |Ψ(x)|² into a single localized position eigenstate, demonstrating how observation alters the physical system.