A minimum-uncertainty wave packet, drawn twice — once in position and once in momentum. Squeeze one curve and the other widens by exactly the same factor, because their product is pinned at h-bar/2. Nothing here measures anything; the trade-off is built into the packet itself.
Product divided by h-bar/2 Δx · Δp ÷ (h-bar/2)
1.00
A Gaussian packet sits exactly on the floor, so this never moves.
Position spread Δx
100 pm
Set by the slider below
Momentum spread Δp
5.27e-25
kg·m/s — same for every particle
Product Δx · Δp
5.27e-35
J·s — h-bar/2 = 5.27e-35 J·s
Speed spread Δv = Δp / m
5.79e5 m/s
Mass divides the momentum spread
Confinement energy E = Δp² / 2m
0.953 eV
The kinetic energy the squeeze costs
Position spread Δx100 pm
Slide left to confine the particle more tightly.
h-bar = 1.054571817e-34 J·s · h-bar/2 = 5.27285909e-35 J·s
me = 9.1093837139e-31 kg · mp = 1.67262192595e-27 kg
Minimum-uncertainty (Gaussian) packet: Δx · Δp = h-bar/2 exactly.
Tip: hold Δx still and switch particle. Δp does not budge — it depends only on how tightly the packet is confined. Only Δv and the energy change, and they change by the mass ratio.