Heisenberg Uncertainty Principle

About the Uncertainty Principle

The Heisenberg uncertainty principle states that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa. This is expressed as Δx·Δp ≥ ℏ/2.

Position Uncertainty Δx (nm) 1.0 nm

Momentum Uncertainty Δp (kg⋅m/s) 5.0×10⁻²⁵ kg⋅m/s

Wave Packet Width 2.0

Measurement Precision 0.5

Position Probability Distribution

Momentum Probability Distribution

Wave Function in Position Space

Δx·Δp Product

5.3×10⁻³⁵

J⋅s

ℏ/2 Limit

5.3×10⁻³⁵

J⋅s

Uncertainty Ratio

1.00

(Δx·Δp)/(ℏ/2)