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Quantum Engineering Year 1: Quantum Mechanics Core Month 13Day 354

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Year 1·Month 13·Week 3

Day 354: Position-Momentum Uncertainty — Δx·Δp ≥ ℏ/2

Day 354 of 2,016~17 min read

Learning Objectives

•Derive Δx·Δp ≥ ℏ/2 from the generalized uncertainty principle
•Identify and construct Gaussian minimum uncertainty wave packets
•Analyze wave packet spreading and its connection to uncertainty
•Calculate uncertainties for various quantum states
•Explain the complementary nature of position and momentum
•Connect the uncertainty relation to diffraction and interference

Today's Schedule (7 hours)

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On this page

1 The Canonical Uncertainty Relation 2 Minimum Uncertainty States Gaussians 3 Position and Momentum Representations 4 Gaussian Wave Packet Detailed Analysis 5 Wave Packet Spreading 6 The Uncertainty Principle and Diffraction 7 Other Conjugate Pairs Physical Interpretation What xp 2 Really Means The Wave-Particle Duality Connection

Day 353Day 354 of 2,016Day 355