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Quantum Engineering Year 1: Quantum Mechanics Core Month 18Day 502

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Year 1·Month 18·Week 4

Day 502: Resonances

Day 502 of 2,016~18 min read

Learning Objectives

•**Explain** the physical origin of resonances
•**Derive** the Breit-Wigner resonance formula
•**Relate** resonance width to lifetime via uncertainty principle
•**Analyze** phase shift behavior through a resonance
•**Identify** resonances in cross section data
•**Apply** resonance concepts to nuclear and particle physics

Today's Schedule (7 hours)

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Overview Schedule Learning Objectives 1 Physical Origin of Resonances What is a Resonance Classical Analogy Quantum Picture Types of Resonances 2 The Breit-Wigner Formula Derivation from Partial Waves The Breit-Wigner Amplitude Breit-Wigner Cross Section Properties of Breit-Wigner S-Matrix at Resonance 3 Width and Lifetime Heisenberg Uncertainty Relation Physical Interpretation Typical Values Time Delay in Scattering 4 Phase Shift Behavior Phase Shift Through Resonance Key Features Graphical Behavior Levinson Connection 5 Background and Interference Resonance Plus Background Fano Resonance Fano Profile Shapes Physical Origin of Asymmetry 6 Worked Examples Example 1 Neutron-Nucleus Resonance Example 2 Phase Shift Analysis Example 3 Z Boson Resonance 7 Practice Problems Level 1 Direct Application Level 2 Intermediate Level 3 Challenging 8 Computational Lab Resonance Analysis 9 Summary Key Concepts Key Formulas 10 Daily Checklist Conceptual Understanding Mathematical Skills Computational Skills 11 Preview Day 503 References

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