A Gaussian wavepacket ψ(x) = A·exp(−x²/4σ_x²)·e^{ik₀x} has a Fourier transform that is also Gaussian: φ(p) ∝ exp(−σ_x²(p−k₀)²/ℏ²). The widths satisfy σ_p = ℏ/(2σ_x), giving Δx·Δp = ℏ/2 exactly — the minimum uncertainty state (coherent state). Any other waveform has Δx·Δp ≥ ℏ/2. Time evolution spreads the packet: σ_x(t)² = σ_x² + (ℏt/2mσ_x)², demonstrating that even a minimum-uncertainty packet acquires position uncertainty over time while conserving the overall uncertainty product.