∆E ∆t ≥ ħTime is a parameter, not an observable. ∆t is some timescale over which the expectation value of an operator changes. For example, an electron's angular momentum in a hydrogen atom decays from 2p to 1s. These decays are relativistic, however the uncertainty principle is still valid, and we can use it to estimate uncertainties.When heavy particles are made in colliders, they typically decay, which gives a linewidth to their measured mass via the uncertainty in energy. The ∆ particle lives very briefly (often called resonances instead of particles), and its lifetime is 5.58 x 10-24 s. Its mass is 1.232 GeV/c2. Predict the width of its energy resonance in MeV.

The objective of the question is to predict the width of the energy resonance of a ∆ particle using…

Answered: ∆E ∆t ≥ ħTime is a parameter, not an…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter28: Quantum Physics

Section: Chapter Questions

Problem 55P

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∆E ∆t ≥ ħ
Time is a parameter, not an observable. ∆t is some timescale over which the expectation value of an operator changes. For example, an electron's angular momentum in a hydrogen atom decays from 2p to 1s. These decays are relativistic, however the uncertainty principle is still valid, and we can use it to estimate uncertainties.

When heavy particles are made in colliders, they typically decay, which gives a linewidth to their measured mass via the uncertainty in energy. The ∆ particle lives very briefly (often called resonances instead of particles), and its lifetime is 5.58 x 10^-24 s. Its mass is 1.232 GeV/c². Predict the width of its energy resonance in MeV.

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