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9/25/2013PHY 711 Fall Lecture 131 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 13: Finish reading Chapter 6 1.Canonical transformations 2.Hamilton-Jacobi formalism

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9/25/2013PHY 711 Fall Lecture 132

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9/25/2013PHY 711 Fall Lecture 133

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9/25/2013PHY 711 Fall Lecture 134

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9/25/2013PHY 711 Fall Lecture 135 Review: Liouville’s theorem: Imagine a collection of particles obeying the Canonical equations of motion in phase space.

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9/25/2013PHY 711 Fall Lecture 136 Proof of Liouville’e theorem:

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9/25/2013PHY 711 Fall Lecture 137

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9/25/2013PHY 711 Fall Lecture 138 0

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9/25/2013PHY 711 Fall Lecture 139 Notion of “Canonical” distributions

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9/25/2013PHY 711 Fall Lecture 1310 Note that it is conceivable that if we were extraordinarily clever, we could find all of the constants of the motion!

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9/25/2013PHY 711 Fall Lecture 1311

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9/25/2013PHY 711 Fall Lecture 1312 Note that it is conceivable that if we were extraordinarily clever, we could find all of the constants of the motion! Possible solution – Hamilton-Jacobi theory:

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9/25/2013PHY 711 Fall Lecture 1313

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9/25/2013PHY 711 Fall Lecture

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9/25/2013PHY 711 Fall Lecture

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9/25/2013PHY 711 Fall Lecture 1316 Differential equation for S:

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9/25/2013PHY 711 Fall Lecture 1317 Continued:

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9/25/2013PHY 711 Fall Lecture 1318 Continued:

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