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Problems 1-6:
Reif, Problems 3.1-3.6

Problem #7 (517 and Honors only):
This problem deals with a system consisting of N weakly interacting quantum harmonic oscillators, with total energy E. The energy of these oscillators is given by

   where     

The number of microstates of this system is the same as the number of ways of arranging M indistinguishable objects in N distinguishable bins. This is

Using this, find expressions for

1. The entropy in terms of N and M
2. The energy in terms of N and T
3. The probability p(n) that the ith oscillator has quantum number n_i=n.