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Quantum Engineering Year 0: Mathematical Foundations Month 12Day 314

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Year 0·Month 12·Week 1

Day 314: Group Theory Synthesis

Day 314 of 2,016~3 min read

Learning Objectives

•Review abstract group theory
•Connect representations to quantum states
•Master Lie groups and algebras
•Apply to angular momentum

Today's Schedule (7 hours)

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Overview Learning Objectives 1 Abstract Groups Axioms Key Results 2 Representations Definition Characters Orthogonality 3 Lie Groups and Algebras Lie Group Lie Algebra Exponential Map Example SU2 4 Angular Momentum Commutation Relations Eigenvalues Addition 5 Physics Applications Selection Rules Atomic Structure 6 Computational Lab Summary The Symmetry QM Pipeline Key Formula Preview Day 315

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