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Quantum Engineering Year 0: Mathematical Foundations Month 11Day 298

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Year 0·Month 11·Week 3

Day 298: The Lie Algebra so(3) and Angular Momentum

Day 298 of 2,016~4 min read

Learning Objectives

•Master the so(3) commutation relations
•Connect to quantum angular momentum operators
•Understand the Casimir operator
•Derive eigenvalue spectra using Lie algebra methods

Today's Schedule (7 hours)

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Overview Learning Objectives 1 The Lie Algebra so3 Definition The Fundamental Commutation Relations 2 Quantum Angular Momentum The Operators Position Space Representation 3 The Casimir Operator Definition Key Property Eigenvalues 4 Ladder Operators Definition Commutation Relations Action on States 5 Representations of so3 Irreducible Representations Matrix Representations 6 Computational Lab Summary Preview Day 299

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