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Quantum Engineering Year 0: Mathematical Foundations Month 6Day 142

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Year 0·Month 6·Week 1

Day 142: The Principle of Least Action

Day 142 of 2,016~12 min read

Learning Objectives

•Understand the concept of functionals and their extrema
•State the Principle of Least Action
•Define the Lagrangian L = T - V
•Derive equations of motion from the action principle
•Connect to Fermat's principle in optics
•Understand the deep connection to quantum mechanics

Today's Schedule (7 hours)

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1 From Newton to Hamiltons Principle 2 Functionals vs Functions 3 The Lagrangian 4 The Action 5 Hamiltons Principle Principle of Least Action 6 Derivation of the Euler-Lagrange Equations 7 Multiple Degrees of Freedom 8 Why Least Action 9 Quantum Mechanics Connection 10 Fermats Principle Optical Analog

Day 141Day 142 of 2,016Day 143