Modern Physics
Heisenberg electron
Tighten Δx or raise K — check Δx·Δp ≥ ℏ/2 on the bar.
Heisenberg electron — interactive Modern Physics simulation. Tighten Δx or raise K — check Δx·Δp ≥ ℏ/2 on the bar. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Uncertainty principle
Tighten Δx or raise K — check Δx·Δp ≥ ℏ/2 on the bar.
Confine an electron to Δx ≈ 0.1 nm (atomic scale). The momentum spread Δp is at least ℏ/(2Δx), so Δx·Δp ≥ ℏ/2. Press Play: the confinement box breathes slightly and the ψ / |ψ|² curves oscillate like a matter-wave packet. Tightening Δx or raising kinetic energy K increases the product shown on the bar.
- ΔxΔp ≥ ℏ/2
- Tradeoff
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
If you confine an electron to a smaller and smaller region of space (reducing the uncertainty in its position), does the minimum possible uncertainty in its momentum shrink too, or grow?
Predictions to weigh
- It grows — position and momentum uncertainty trade off against each other; confining position more precisely forces momentum to become less certain.
- It shrinks along with position uncertainty.
- Momentum uncertainty doesn't depend on position uncertainty.
Variable roles
What you set:
- Position uncertainty Δx (nm)
What you measure:
- Momentum uncertainty Δp (×10⁻²⁵ kg·m/s)
How the investigation runs
- Open the heisenberg-electron preset and press Reset.
- Enable the minimum-momentum-uncertainty readout.
- Set the position uncertainty Δx for each trial and record the minimum possible momentum uncertainty.
Governing equation
Heisenberg Uncertainty Principle — Δx·Δp ≥ ℏ/2
Position and momentum can never both be known with unlimited precision simultaneously: Δx·Δp ≥ ℏ/2, where ℏ = h/2π. A more precisely known position forces momentum to become correspondingly less certain.
What the printable worksheet asks students to work out
- For one trial, compute Δp_min = ℏ/(2Δx) using ℏ = 1.055×10⁻³⁴ J·s. Compare to the table.
- Explain why the product Δx·Δp_min is exactly the same (ℏ/2) in every trial — the uncertainty principle sets a fixed lower bound on the PRODUCT of the two uncertainties, not on either one alone.
Where this shows up beyond the lab
- The uncertainty principle isn't about clumsy measuring instruments disturbing a particle — it's a fundamental property of quantum states themselves, true even with perfect measuring equipment. Explain why 'measurement disturbance' is a common but incomplete way to describe this principle.
- For a baseball (much more massive than an electron), confining its position to within a millimeter still gives an absurdly tiny minimum momentum uncertainty compared to its actual momentum. Explain why quantum uncertainty is only noticeable for very light particles like electrons.
- AP Physics 2 — Unit 15: Modern Physics
- IB Physics — E.2 Quantum physics
- General High School Physics — Modern physics intro
- NGSS High School Physics — Wave-particle duality of light
- Welcome to Heisenberg Electron
- Select the uncertainty setup
- Press Play
- Spread in x and p
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.