1. 8/28/2015PHY 711 Fall 2015 -- Lecture 21 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 2: 1. Brief comment on quiz 2. Particle interactions 3.Notion of center of mass reference fame 4.Introduction to scattering theory

2. 8/28/2015PHY 711 Fall 2015 -- Lecture 22

3. 8/28/2015PHY 711 Fall 2015 -- Lecture 23 Comment on quiz questions 1. 3.

4. 8/28/2015PHY 711 Fall 2015 -- Lecture 24 Classical mechanics of a conservative 2-particle system. 1 2

5. 8/28/2015PHY 711 Fall 2015 -- Lecture 25 Relationship between center of mass and laboratory frames of reference

6. 8/28/2015PHY 711 Fall 2015 -- Lecture 26 Classical mechanics of a conservative 2-particle system -- continued

7. 8/28/2015PHY 711 Fall 2015 -- Lecture 27 Note: The following analysis will be carried out in the center of mass frame of reference. In laboratory frame: In center-of-mass frame: V1V1 m1m1 m target v1v1  origin v CM r Also note: We are assuming that the interaction between particle and target V(r) conserves energy and angular momentum.

8. 8/28/2015PHY 711 Fall 2015 -- Lecture 28 Scattering theory:

9. 8/28/2015PHY 711 Fall 2015 -- Lecture 29 Figure from Marion & Thorton, Classical Dynamics b

10. 8/28/2015PHY 711 Fall 2015 -- Lecture 210 Simple example – collision of hard spheres Microscopic view:

11. 8/28/2015PHY 711 Fall 2015 -- Lecture 211 E r min For a continuous potential interaction’ in center of mass reference frame: V(r)

12. 8/28/2015PHY 711 Fall 2015 -- Lecture 212 r min r  

13. 8/28/2015PHY 711 Fall 2015 -- Lecture 213

14. 8/28/2015PHY 711 Fall 2015 -- Lecture 214

15. 8/28/2015PHY 711 Fall 2015 -- Lecture 215

16. 8/28/2015PHY 711 Fall 2015 -- Lecture 216 Figure from Marion & Thorton, Classical Dynamics b

17. 8/28/2015PHY 711 Fall 2015 -- Lecture 217

18. 8/28/2015PHY 711 Fall 2015 -- Lecture 218

19. 8/28/2015PHY 711 Fall 2015 -- Lecture 219 Relationship between  max and 

20. 8/28/2015PHY 711 Fall 2015 -- Lecture 220

21. 8/28/2015PHY 711 Fall 2015 -- Lecture 221

22. 8/28/2015PHY 711 Fall 2015 -- Lecture 222