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Quantum Engineering Year 0: Mathematical Foundations Month 7Day 190

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Year 0·Month 7·Week 4

Day 190: Green's Functions and Propagators

Day 190 of 2,016~6 min read

Learning Objectives

•Define Green's functions as inverses of differential operators
•Compute Green's functions using contour integration
•Understand the resolvent and its analytic properties
•Relate poles to bound states and branch cuts to continua
•Calculate propagators for free particles
•Apply the $+i\varepsilon$ prescription for causality

Today's Schedule (7 hours)

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1 Greens Functions Definition 2 The Resolvent Operator 3 Free Particle Propagator 4 The ivarepsilon Prescription 5 Contour Integral Computation 6 Time-Dependent Propagator

Day 189Day 190 of 2,016Day 191