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Quantum Engineering Year 0: Mathematical Foundations Month 8Day 207

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Year 0·Month 8·Week 2

Day 207: Magnetic Vector Potential

Day 207 of 2,016~12 min read

Learning Objectives

•Define the magnetic vector potential and explain why it exists
•Derive $\mathbf{B} = \nabla \times \mathbf{A}$ and verify Maxwell's equations
•Understand gauge freedom and the Coulomb gauge
•Calculate $\mathbf{A}$ for common current distributions
•Explain the Aharonov-Bohm effect and minimal coupling
•Connect to the quantum mechanical momentum operator

Today's Schedule (7 hours)

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On this page

1 Why a Vector Potential 2 The Vector Potential from Currents 3 Gauge Freedom 4 Coulomb Gauge 5 Other Gauges 6 Examples of Vector Potential 7 Multipole Expansion of mathbfA 8 Magnetic Flux and mathbfA Quantum Mechanics Connection Minimal Coupling The Central Role of mathbfA The Aharonov-Bohm Effect Gauge Invariance in QM Landau Levels Revisited

Day 206Day 207 of 2,016Day 208