homework6

homework6 - 2. Using the power series representation of J p...

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Homework 6 PHZ 5156 Due Thursday, October 26 1. Consider a system with two states with energies E 1 = - ± and E 2 = ± , in thermal equilibrium with an external heat bath at temperature T . Recall that the partition function is given by Z = Tr exp ( - E k B T ) (trace is a sum over the possible states), the free energy is F = - k B TlogZ , and the heat capacity is given by C = - T 2 F ∂T 2 . Compute the heat capacity of the two-level system.
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Unformatted text preview: 2. Using the power series representation of J p ( x ) and J-p valid for non-integer p, show that r x 2 J-1 2 ( x ) = cosx 3. Using the power series representation of J p ( x ) and J-p , show that J 3 2 ( x ) = 1 x J 1 2 ( x )-J-1 2 ( x ) 4. Using the power series representation of J p ( x ), show that d dx x-p J p ( x ) =-x-p J p +1 ( x ) 1...
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