Quantic vs Classic world

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Quantic vs Classic world
What defines the granular nature of our Universe?
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?
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Going classical.
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?
We can obtain the states energies by solving the
classical Hamiltonian equations
We count the states by analogy to the quantum
treatment
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Example I Harmonic Oscillator
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Example II translations
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Example III rotations
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Generalization of the classical treatment
Comparing the high T limit of the QM Stat.Mech.
with classical Stat. Mech. we infer the constants
We are establishing a correspondence principle
between QM and Classical Statistical Mechanics
?
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N particle systems
Consider N interacting particles Each particle
has s degrees of freedom
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Ensembles
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Density number
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Liouville equation
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Liouville eq II
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Liouville eq III
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Net flow in all directions
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Full derivative of f(p,q,t)
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Constant density concept
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No crossing of trajectories