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Quantum Engineering Year 0: Mathematical Foundations Month 6Day 151

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Year 0·Month 6·Week 2

Day 151: Small Oscillations — Normal Modes

Day 151 of 2,016~7 min read

Learning Objectives

•Linearize equations of motion near equilibrium
•Set up the eigenvalue problem for normal modes
•Find normal mode frequencies and eigenvectors
•Understand the general solution as superposition of modes
•Apply to molecular vibrations and coupled systems
•Connect to quantum mechanics (phonons, molecular spectra)

Today's Schedule (7 hours)

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On this page

1 Motivation Why Small Oscillations 2 Equilibrium and Stability 3 Kinetic and Potential Energy Matrices 4 Equations of Motion 5 Normal Mode Ansatz 6 Normal Mode Frequencies and Vectors 7 General Solution 8 Example Two Coupled Pendulums 9 Quantum Connection Practice Problems Level 1 Level 2 Level 3

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