PhysicsChapter 7: Quantum Physics
Heisenberg Uncertainty Principle
The Heisenberg uncertainty principle
Definition
The Heisenberg uncertainty principle states that certain pairs of physical quantities, such as position and momentum, cannot simultaneously have arbitrarily precise values in a quantum state.
Meaning
For position `x` and momentum `pₓ`: Δx Δpₓ ≥ ħ/2 where: ħ = h2π An equivalent common form is: ΔxΔpₓ ≥ h4π If position uncertainty is reduced: **momentum uncertainty must increase** and vice versa. This is not merely poor instrument design. It is a fundamental feature of quantum physics.
Energy-Time Relation
A common uncertainty relation is: **ΔE Δt ≥ ħ/2**
Why Important?
It means classical ideas of simultaneously exact position and momentum do not apply to quantum systems in the same way.
Formula / Key Relation
**ΔxΔp ≥ ħ/2 ΔEΔt ≥ ħ/2**
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Review the key facts, formulas and checks before you move on.Heisenberg Uncertainty Principle
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UNCERTAINTY
- `Δx ↓ → Δp ↑`
- `ΔxΔp ≥ ħ/2`
60-second revision
- Quantum precision has fundamental limits for conjugate quantities.
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