Physics 418: Statistical Mechanics I Set3 Hint1To deal with the fact that the variables y_{i} interact with each other, transform to new variables, w_{i} = y_{i}  y_{i1} The constraint on the endpoints then becomes
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.)


Last update: Wednesday, August 22, 2007 at 1:08:22 PM. 