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Energy–time uncertainty
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Short-lived states have uncertain energy.
ΔEΔt ≥ ħ/2ΔEΔt ≥ ħ/2: a state that lives only for Δt has an energy spread. Explains natural line widths and virtual particles.
An excited state with a 10 ns lifetime has ΔE ≈ 3×10⁻⁸ eV.
Time isn't an operator in the same way as position.
In more detail
An energy-time uncertainty relation ΔE Δt ≥ ħ/2 limits how precisely the energy of a state can be known over a short time. Short-lived states have broad energy spreads.
Real-world uses
- Particle lifetimes are linked to their energy widths.
- Spectral line widths depend on the lifetime of excited states.
- Physicists explain why unstable particles and excited atomic states have a spread in their measured energies.
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Frequently asked questions
What does it imply for short-lived particles?
They have broad, uncertain masses, which appear as wide resonance peaks.
Is time an observable?
In quantum mechanics, time is a parameter rather than an operator, which is why this relation is different in form.
Why does a short-lived state have a broad line?
A short lifetime means a large uncertainty in energy, which broadens the spectral line.
Related topics in Quantum Mechanics
Wave–particle duality · Double slit with electrons · Heisenberg uncertainty principle · Wavefunction · Born rule · Normalisation