1. 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 Chapter 6 1.Canonical transformations 2.Hamilton-Jacobi formalism

2. 9/25/2013PHY 711 Fall 2013 -- Lecture 132

3. 9/25/2013PHY 711 Fall 2013 -- Lecture 133

4. 9/25/2013PHY 711 Fall 2013 -- Lecture 134

5. 9/25/2013PHY 711 Fall 2013 -- 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 2013 -- Lecture 136 Proof of Liouville’e theorem:

7. 9/25/2013PHY 711 Fall 2013 -- Lecture 137

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

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

10. 9/25/2013PHY 711 Fall 2013 -- 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 2013 -- Lecture 1311

12. 9/25/2013PHY 711 Fall 2013 -- 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 2013 -- Lecture 1313

14. 9/25/2013PHY 711 Fall 2013 -- Lecture 1314 0 00

15. 9/25/2013PHY 711 Fall 2013 -- Lecture 1315 0 00

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

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

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