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Quantum Engineering Year 0: Mathematical Foundations Month 7Day 191

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Year 0·Month 7·Week 4

Day 191: Dispersion Relations and Causality

Day 191 of 2,016~5 min read

Learning Objectives

•Derive Kramers-Kronig relations from contour integration
•Understand the connection between analyticity and causality
•Apply dispersion relations to physical response functions
•Derive and interpret sum rules
•Connect to the optical theorem in scattering
•Apply to refractive index and conductivity

Today's Schedule (7 hours)

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1 Causality and Analyticity 2 Kramers-Kronig Relations 3 Physical Interpretation 4 Sum Rules 5 Optical Theorem 6 Applications Refractive Index Dielectric Function

Day 190Day 191 of 2,016Day 192