Modern Physics
Heisenberg Uncertainty Principle
Position and momentum cannot both be precisely known. Fundamental limit of measurement.
Variables
Δxm
Position uncertainty
Δpkg·m/s
Momentum uncertainty
ℏJ·s
Reduced Planck constant
Derivation
Arises from the wave nature of matter and the commutation relation [x,p] = iℏ.
Your notes
0/5000
Constants in this formula
Other modern physics formulas with the same quantities
- Time-Dependent Schrödinger Equation (Quantum Mechanics) shares Reduced Planck constant
- Fermi Energy (Quantum Mechanics) shares Reduced Planck constant
- Bohr Radius (Atomic Physics) shares Reduced Planck constant
Where this formula is listed
- Modern Physics formulas, under Quantum Mechanics, alongside Photon Energy (Planck), Photoelectric Effect, Stopping Potential, Particle in a Box Energy Levels and Compton Scattering.
- In the modern physics list it comes after de Broglie Wavelength and before Energy-Time Uncertainty.
- Modern Physics formula sheet, one of 41 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
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, Δx is position uncertainty, measured in m; Δp is momentum uncertainty, measured in kg·m/s; ℏ 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.