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Quantum Engineering Year 0: Mathematical Foundations Month 7Day 184

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Year 0·Month 7·Week 3

Day 184: Classification of Singularities

Day 184 of 2,016~14 min read

Learning Objectives

•Classify isolated singularities as removable, poles, or essential
•Apply Riemann's theorem on removable singularities
•Determine the order of a pole
•Apply the Casorati-Weierstrass theorem for essential singularities
•Connect singularity classification to Laurent series structure
•Relate poles to resonances in quantum scattering theory

Today's Schedule (7 hours)

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On this page

1 Isolated Singularities Definition and Overview 2 The Three Types of Isolated Singularities 3 Removable Singularities 4 Poles 5 Essential Singularities 6 The Casorati-Weierstrass Theorem 7 Summary Table Quantum Mechanics Connection Poles in Scattering Amplitudes Resonances as Complex Poles Greens Function Poles Essential Singularities in QM

Day 183Day 184 of 2,016Day 185