Re: Accessible States

[James McLean <jmclean@CHEM.UCSD.EDU>]

Jim Green wrote:
> ...
> Now Vp = (4/3)pi x p(max)^3    &   p(max) = sqrt(2mE)
>
> So Omega(1) = (4/3)pi(2m)^(3/2) x V E^(3/2)
>
> Now Omega(N) =Prod[Omega(i)]
>
> So Omega(N) = Const x V^N x E^(3N/2)    Cf big Rief Eqn 2.5.19
> ...

For those interested in nit-picking:
This doesn't quite work, because you have now allowed each atom to have
up to energy E, for a total possible energy of N*E.  Instead of N times
the volume of a sphere in 3-dim p-space, you need the volume of a
spherical shell in 3*N-dim p-space.  The exponent on E in the last
equation then becomes (3N-1)/2.

Note that Reif actually gets this wrong:  his Eqn 2.5.18 uses (3N/2)-1
instead of (3N-1)/2.  But since, as he notes, the 1 can be ignored
relative to N, the whole point is moot, and you get his Eqn 2.5.19 at
the end of the day regardless of which path you take.

Now back to discussing the quantum aspects of the problem....
--
--James McLean
jmclean@chem.ucsd.edu
post doc, UC San Diego, Chemistry
moving to SUNY Geneseo Physics this fall