Heisenberg–Fourier Uncertainty Principle

Δx · Δk ≥ ½ · · · Gaussian wavepackets minimize uncertainty

Position space |ψ(x)|²

Wavepacket type: Width σ (position): 0.12 Carrier frequency k₀: 8 Window (spectrogram): 0.10

Δx (std):—

Δk (std):—

Δx·Δk:—

Minimum (½):0.500

Frequency space |ψ̂(k)|² — Fourier transform

Spectrogram (STFT) — time-frequency trade-off