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9/25/2013PHY 711 Fall 2013 -- Lecture 131 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 13: Finish reading.

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Presentation on theme: "9/25/2013PHY 711 Fall 2013 -- Lecture 131 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 13: Finish reading."— Presentation transcript:

1 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

2 9/25/2013PHY 711 Fall Lecture 132

3 9/25/2013PHY 711 Fall Lecture 133

4 9/25/2013PHY 711 Fall Lecture 134

5 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.

6 9/25/2013PHY 711 Fall Lecture 136 Proof of Liouville’e theorem:

7 9/25/2013PHY 711 Fall Lecture 137

8 9/25/2013PHY 711 Fall Lecture 138 0

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

10 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!

11 9/25/2013PHY 711 Fall Lecture 1311

12 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:

13 9/25/2013PHY 711 Fall Lecture 1313

14 9/25/2013PHY 711 Fall Lecture

15 9/25/2013PHY 711 Fall Lecture

16 9/25/2013PHY 711 Fall Lecture 1316 Differential equation for S:

17 9/25/2013PHY 711 Fall Lecture 1317 Continued:

18 9/25/2013PHY 711 Fall Lecture 1318 Continued:


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