Why Isn't the Density of States for a Bose Gas Infinite?

[ehrenfest]

[SOLVED] density of states for a Bose gas

Homework Statement

My book (Kittel) says that the density of states of an ideal Bose gas is:$$D(\epsilon) = V/4\pi^2 \left(2M/\hbar^2 \right)^{3/2} \epsilon^{1/2}$$

I do not understand why the density of states is not identically infinity since the point of a Bose gas is that an orbital can be occupied by an unlimited number of bosons.

Homework Equations

The Attempt at a Solution

 

[malawi_glenn]

Because the the distribution function is given by:

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/disbe.html

http://en.wikipedia.org/wiki/Bose-Einstein_statistics

Remeber that at a certain temperature, particles can be excitet to a higher state.

I mean photons are bosons, but the density of the radiation field is not infinite.

And in fermi statistics, just because you CAN have maximum ONE particle/state does not mean that you HAVE it.

 

[genneth]

The definition of density of states for quantum gases is usually for a single particle.