Problem 1 (10 points) _
There are two particles in a two level system. The energy levels of the system is E; = e6, 6.
(a) Find the probability, p;- (as a function of temperature) that a particle has energy Ei.
(b) What is the free energy per particle? -
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Problem 2 'Ilw ltllllh'ulll solid picture assumoi that atom 2' of a solid sits at lattice position
rm and can oscillate harmonically around this position. it is described by the Hamiltonian
H p2 1 N 2
m2 _"_ m- 2E. .w. o 1
H on 2m 4 2m 12:01 re.) ( J
(a)