How is the Number of Quantum States Derived for Combined Einstein Solids?

[loonychune]

Two Einstein solids are joined so that they can exchange energy. One contains N_A oscillators, the other N_B oscillators. Apparently, the possible number of quantum states of the combined system is given by,

$$g(n,N) = \sum_{n_A = 0}^n g(N_A,n_A)g(N_B,n-n_A)$$

where n is the principal quantum number of the composite solid

$$n = n_A + n_B$$

Now, I cannot see where this comes from. I hope this formula looks familiar more than anything, though I will look to write up everything I see here contained in the notes if necessary. Can anyone help?

Thanks,


Damian

 

[loonychune]

Actually, I see it now.

Bringing the two systems into thermal contact means they can exchange energy, so we have to sum over all the possible discrete energies.

e.g.

$$n_A = 3, n_B = 4 \rightarrow n_{A,NEW} = 0, n_{B,NEW} = 7$$

is a new possible arrangement.