Modern Physics
Heisenberg Uncertainty Principle
Position and momentum cannot both be precisely known. Fundamental limit of measurement.
Variables
\Delta xm
Position uncertainty
\Delta pkg·m/s
Momentum uncertainty
\hbarJ·s
Reduced Planck constant
Derivation
Arises from the wave nature of matter and the commutation relation [x,p] = iℏ.
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Common questions
What is the Heisenberg Uncertainty Principle formula?
Heisenberg Uncertainty Principle is written Δx ·Δp ≥ℏ/2. Position and momentum cannot both be precisely known. Fundamental limit of measurement. It belongs to Modern Physics, under Quantum Mechanics.
What are the units in Δx ·Δp ≥ℏ/2?
In SI units, \Delta x is position uncertainty, measured in m; \Delta p is momentum uncertainty, measured in kg·m/s; \hbar is reduced planck constant, measured in J·s.
How is the Heisenberg Uncertainty Principle formula derived?
Arises from the wave nature of matter and the commutation relation [x,p] = iℏ. The result is Δx ·Δp ≥ℏ/2.