# Between classical or quantum statistics

1. Apr 22, 2005

### GotTrips

Hi can someone please help me! Can someone explain when it is acceptable to quantum statistics instead of classical statistics? And what is the difference between them.

Thanks All

OLY

2. Apr 22, 2005

### infra

I dont remember the eqn but the critical word is "thermal wave length" that describes the difference between two. Look at th Huang's Statistical Mechenics for details

3. Apr 24, 2005

### dextercioby

Microscopical dynamics and the application of the 6 postulates of (nonrelativistic) QM is the decisive factor...

Think of the Gibbs' paradox and u'll understand the need for a quantum statistical physics...

Daniel.

4. Apr 25, 2005

### seratend

Seratend.

5. Apr 25, 2005

### dextercioby

The Gibbs paradox is accounted for quite nicely even in classical statistic if one considers the dimensionless volume element on the phase space

$$d^{2s}\tilde{x}=:\frac{1}{h^{2s}}\prod_{i=1}^{2s} dq_{i}dp_{i}$$

to which the VI-th postulate is applied to

$$d^{2x}x^{*}=:\frac{1}{h^{2s}N!}\prod_{i=1}^{2s} dq_{i}dp_{i}$$

Daniel.

Last edited: Apr 25, 2005