Physical Sciences

Quantum Mechanics

1927

Advanced

Heisenberg Uncertainty Principle

\Delta x \, \Delta p \geq \frac{\hbar}{2}

You cannot simultaneously know a particle's position and momentum with arbitrary precision.

By Werner Heisenberg

Physical Sciences

1927 · Werner Heisenberg

Human Reviewed

84%

Rabbit Hole Mode

Five doors into the universe behind this equation. Choose your path.

Story PortalWho discovered this?Discover how Werner Heisenberg and others shaped this equation.Visual PortalWhat does it look like?See the equation come alive in the Visual Studio.Machine PortalWhere is it used?Explore machines powered by this equation — electron microscopy limits.Math PortalWhat does it derive from?Trace the mathematical lineage from schrodinger equation.Future PortalWhere is it going?Quantum sensing at fundamental limits

Launch collection — full story, visual, sound & share card

Why it matters: Ended classical determinism at atomic scales; enabled quantum technology.

Discoverers: Werner Heisenberg (1927)

What does it mean?

You cannot simultaneously know a particle's position and momentum with arbitrary precision.

Why should I care?

Ended classical determinism at atomic scales; enabled quantum technology.

Equation Compass

North — Prerequisites

Schrödinger Equation

West — History

Werner Heisenberg

East — Applications

South — Derivations

Derivation

Variables & Units

Symbol	Name	Unit	Meaning
$Δx$	Position uncertainty	m	Spread in position
$Δp$	Momentum uncertainty	kg·m/s	Spread in momentum

Worked Example

Electron confined to atom (~10⁻¹⁰ m) has momentum uncertainty ~10⁻²⁴ kg·m/s.

AI Guide (Pro)

Ask questions about equations and get answers grounded in the Equation Universe catalog.

Upgrade to Pro Try demo (7 days)

Sources & further reading

Search Wikipedia Search Wolfram MathWorld Open in Wolfram|Alpha Watch explainers on YouTube

Equation Universe