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Quantum Engineering Year 0: Mathematical Foundations Month 11Day 296

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Year 0·Month 11·Week 3

Day 296: The Rotation Group SO(3)

Day 296 of 2,016~4 min read

Learning Objectives

•Parameterize SO(3) using axis-angle and Euler angles
•Derive Rodrigues' rotation formula
•Understand the topology of SO(3)
•Connect rotations to angular momentum operators
•Compute rotation matrices from different parameterizations

Today's Schedule (7 hours)

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Overview Learning Objectives 1 SO3 The Special Orthogonal Group Definition Rotation Generators 2 Parameterizations of SO3 Axis-Angle Parameterization Euler Angles ZYZ Convention Quaternion Representation 3 Topology of SO3 SO3 is NOT Simply Connected Universal Cover SU2 4 Angular Momentum Connection Quantum Mechanical Angular Momentum Spherical Harmonics 5 Computational Lab 6 Summary Preview Day 297

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