Uncertainty Principle

▸ Building a Gaussian wave packet in position space ψ(x)…

▸ Fourier transform → momentum distribution |φ(p)|²

▸ Calibrating the relation Δx·Δp ≥ ℏ/2 (Heisenberg)

▸ Loading the energy–time form ΔE·Δt & zero-point energy…

▸ Distinguishing intrinsic wave nature ≠ measurement effect

▸ Ready — Online. ✅

Current state

⚖️ Cân bằng Δx ≈ Δp

Position uncertainty—

Momentum uncertainty—

Uncertainty product—

Vs. the minimum—

Localization—

Quantum note

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Drag Localization on the right: squeeze the position packet narrow → the momentum spectrum bulges wide · switch Scenarios to see E–t, zero-point, tunnelling.

Position wave packet ψ(x) & momentum distribution |φ(p)|² ψ(x)|φ(p)|²