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Quantum Engineering Year 1: Quantum Mechanics Core Month 15Day 408

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Year 1·Month 15·Week 3

Day 408: Coupled vs Uncoupled Basis

Day 408 of 2,016~6 min read

Learning Objectives

•Write states in the uncoupled basis |j₁,m₁;j₂,m₂⟩
•Write states in the coupled basis |j,m;j₁,j₂⟩
•Understand when to use each basis
•Describe the unitary transformation between bases
•Count states and verify dimensions

Today's Schedule (7 hours)

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1 The Uncoupled Product Basis 2 The Coupled Basis 3 Which Operators Commute 4 The Basis Transformation 5 Selection Rule Quantum Computing Connection

Day 407Day 408 of 2,016Day 409