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Quantum Engineering Year 0: Mathematical Foundations Month 11Day 300

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Year 0·Month 11·Week 3

Day 300: Representations of SU(2) — All Spins

Day 300 of 2,016~4 min read

Learning Objectives

•Classify all irreps of SU(2)
•Construct representations using ladder operators
•Connect to quantum mechanical spin
•Master the Clebsch-Gordan coefficients

Today's Schedule (7 hours)

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Overview Learning Objectives 1 Classification of Irreps The Main Result Why Both Integer and Half-Integer 2 Construction Using Ladder Operators The Algebra Building the Representation Normalization 3 Matrix Representations Spin-12 j 12 Spin-1 j 1 4 Tensor Products and Clebsch-Gordan Tensor Product Decomposition Clebsch-Gordan Coefficients 5 Physical Applications Electron Spin Two-Electron Coupling 6 Computational Lab Summary Irreducible Representations of SU2 Key Formulas Preview Day 301

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