Quantic vs Classic world

1. What defines the granular nature of our Universe? Quantic vs Classic world Our classical “behavior” vs the atomic “quantum” characteristics are a consequence of the absolute size of h So far, we “solved” the Q.M. problem and then count all states to get the partition function Q. While trying to count states, we invoke the classical limit and  Can we obtain Q assuming classical behavior for the H? What do you expect to be “different” between the 2 answers?

2. So far, we “solved” the Q.M. problem and then count all states to get the partition function Q. While trying to count states, we invoke the classical limit and  Going classical…. Can we obtain Q assuming classical behavior for the H? We can obtain the states energies by solving the classical Hamiltonian equations We count the states by analogy to the quantum treatment…

3. Example I: Harmonic Oscillator

4. Example II: translations

5. Example III: rotations

6. Comparing the high T limit of the QM Stat.Mech. with classical Stat. Mech. we infer the constants Generalization of the classical treatment We are establishing a “correspondence principle” between QM and Classical Statistical Mechanics 

7. Consider N interacting particles: Each particle has s degrees of freedom N particle systems

8. Ensembles

9. Density number

10. N N’ q1 q1 dq1 q1+dq1 Liouville equation

11. Liouville eq II

12. Liouville eq III

13. Net flow in all directions

14. Full derivative of f(p,q,t)

15. Volume around po,qo with dN in the surface Volume around p,q dN dN Constant density concept

16. No crossing of trajectories