Modern Physics

Heisenberg Uncertainty Principle

Position and momentum cannot both be precisely known. Fundamental limit of measurement.

Variables

\Delta x
Position uncertainty
m
\Delta p
Momentum uncertainty
kg·m/s
\hbar
Reduced Planck constant
J·s

Derivation

Arises from the wave nature of matter and the commutation relation [x,p] = iℏ.

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