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Quantum Engineering Year 1: Quantum Mechanics Core Month 18Day 503

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Year 1·Month 18·Week 4

Day 503: Optical Theorem

Day 503 of 2,016~18 min read

Learning Objectives

•**Derive** the optical theorem from S-matrix unitarity
•**State** the relationship between Im[f(0)] and σ_tot
•**Explain** the physical interpretation as shadow scattering
•**Apply** the optical theorem to verify cross section calculations
•**Connect** to dispersion relations and causality
•**Understand** extensions to inelastic and multi-channel scattering

Today's Schedule (7 hours)

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Overview Schedule Learning Objectives 1 Unitarity The Foundation Probability Conservation S-Matrix Unitarity Elastic Scattering Multi-Channel Unitarity 2 Derivation of the Optical Theorem From Partial Wave Expansion Taking the Imaginary Part The Optical Theorem Alternative Derivation Direct from Unitarity 3 Physical Interpretation Shadow Scattering Wave Interference Picture Mathematical Picture Optical Origin of the Name 4 Applications Application 1 Consistency Check Application 2 Forward Dispersion Relations Application 3 High-Energy Scattering Application 4 Total Cross Section from Forward Scattering 5 Extensions Inelastic Scattering Partial Cross Sections Generalized Optical Theorem Absorptive Scattering 6 Worked Examples Example 1 Verifying the Optical Theorem Example 2 High-Energy Limit Example 3 Black Disk 7 Practice Problems Level 1 Direct Application Level 2 Intermediate Level 3 Challenging 8 Computational Lab Optical Theorem Verification 9 Summary Key Concepts Key Formulas 10 Daily Checklist Conceptual Understanding Mathematical Skills Computational Skills 11 Preview Day 504 References

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