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Physics 418: Statistical Mechanics I
Prof. S. Teitel stte@pas.rochester.edu ----- Spring 2005

Set3 Hint1

To deal with the fact that the variables y_i interact with each other, transform to new variables,

w_i = y_i - y_i-1

The constraint on the endpoints then becomes

L i=1

wi

= Y

If you now write the Hamiltonian in terms of the w_i, the partition function would factor into a product of independent pieces, if it were not for the above constraint on the sum of the w_i.

If you can't figure out how to handle the constraint, here is another hint.

(The above transformation works well for part (b) also.)