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Total Number of Quantum States

  1. Dec 30, 2008 #1
    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,

    [tex]g(n,N) = \sum_{n_A = 0}^n g(N_A,n_A)g(N_B,n-n_A)[/tex]

    where n is the principal quantum number of the composite solid

    [tex]n = n_A + n_B[/tex]

    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
     
  2. jcsd
  3. Dec 31, 2008 #2
    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.

    [tex] n_A = 3, n_B = 4 \rightarrow n_{A,NEW} = 0, n_{B,NEW} = 7 [/tex]

    is a new possible arrangement.
     
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