Physics » Introduction to Quantum Physics » Probability: The Heisenberg Uncertainty Principle

# Summarizing Probability

## Summary of Probability: The Heisenberg Uncertainty Principle

• Matter is found to have the same interference characteristics as any other wave.
• There is now a probability distribution for the location of a particle rather than a definite position.
• Another consequence of the wave character of all particles is the Heisenberg uncertainty principle, which limits the precision with which certain physical quantities can be known simultaneously. For position and momentum, the uncertainty principle is $$\Delta x\Delta p\ge \cfrac{h}{4\pi }$$, where $$\Delta x$$ is the uncertainty in position and $$\Delta p$$ is the uncertainty in momentum.
• For energy and time, the uncertainty principle is $$\Delta E\Delta t\ge \cfrac{h}{4\pi }$$ where $$\Delta E$$ is the uncertainty in energy and $$\Delta t$$ is the uncertainty in time.
• These small limits are fundamentally important on the quantum-mechanical scale.

## Glossary

### Heisenberg’s uncertainty principle

a fundamental limit to the precision with which pairs of quantities (momentum and position, and energy and time) can be measured

### uncertainty in energy

lack of precision or lack of knowledge of precise results in measurements of energy

### uncertainty in time

lack of precision or lack of knowledge of precise results in measurements of time

### uncertainty in momentum

lack of precision or lack of knowledge of precise results in measurements of momentum

### uncertainty in position

lack of precision or lack of knowledge of precise results in measurements of position

### probability distribution

the overall spatial distribution of probabilities to find a particle at a given location