Interactive quantum wave packet simulation · position & momentum space
Position Space ψ(x)Δx = 60 nm
Momentum Space φ(p)Δp = 0.0083 ħ/nm
Position Width Δx60 nm
Carrier Wavenumber k₀3.0 /nm
Δx · Δp—≥ ħ/2 = 0.500 ħ
—Minimum uncertainty at Gaussian packet
Show |ψ|² probability density
Overlay |ψ(x)|² on position plot
t = 0.00 ħ/eV
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The Mathematics
A Gaussian wave packet saturates the uncertainty bound. Its momentum-space transform φ(p) is also Gaussian, with width σ_p = ħ/(2σ_x). Any other shape has a strictly larger product.
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Not Measurement Error
This is not about clumsy instruments. A particle simply does not simultaneously possess a well-defined position and momentum. The uncertainty is ontological, not epistemic.
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Dispersion
Press Evolve to watch time evolution. Momentum components travel at different speeds (v = p/m), spreading the packet. Narrower in x → wider in p → disperses faster.