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Quantum Engineering Year 0: Mathematical Foundations Month 11Day 304

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Year 0·Month 11·Week 4

Day 304: Spin Angular Momentum

Day 304 of 2,016~12 min read

Learning Objectives

•Understand spin as intrinsic angular momentum
•Master the spin-1/2 formalism and Pauli matrices
•Analyze the Stern-Gerlach experiment
•Describe spin states on the Bloch sphere
•Connect to quantum computing qubits

Today's Schedule (7 hours)

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Overview Learning Objectives 1 The Discovery of Spin The Stern-Gerlach Experiment 1922 Goudsmit and Uhlenbeck 1925 2 Spin Algebra The Operators Eigenvalue Equations Key Difference from Orbital 3 Spin-12 The Two-State System State Space The Pauli Matrices Pauli Matrix Properties 4 Measuring Spin Components Eigenstates of hatS_z Eigenstates of hatS_x Eigenstates of hatS_y Sequential Measurements 5 The Bloch Sphere General Pure State The Bloch Vector Expectation Values Key States on Bloch Sphere Orthogonal States 6 Spin Rotations Rotation Operator Examples The 2pi Rotation Phase 7 Magnetic Moment and Stern-Gerlach Magnetic Moment Energy in Magnetic Field Energy Levels Stern-Gerlach Force 8 Larmor Precession Time Evolution Precession of Expectation Values 9 Computational Lab 10 Practice Problems Problem 1 Pauli Matrix Identity Problem 2 General Spin State Problem 3 Rotation Operator Problem 4 Sequential Measurements Problem 5 Larmor Period Summary Spin-12 Formalism The Bloch Sphere Key Properties Preview Day 305

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