- #1
dumbperson
- 77
- 0
Homework Statement
Show that PV = E
Homework Equations
[tex] E= \int^\infty_0 D(\epsilon)n_{FD}(\epsilon) \epsilon \cdot d\epsilon[/tex]
[tex]n_{FD}=\frac{1}{(1+ e^{-(\alpha +\beta \epsilon_k)})}[/tex]
[tex]\psi(\alpha ,\beta, V) =\beta PV =\sum_\vec{k} \ln{(1+e^{-(\alpha +\beta \epsilon_k)}) }[/tex]
and in an earlier problem I found that
[tex] D= \frac{A\cdot m \cdot (2s+1)}{2\pi \hbar^2 } [/tex]
The Attempt at a Solution
I think I'm supposed to wirte $$ \frac{\psi}{\beta }$$ as an integral over $$\epsilon$$ and then compare it to the integral for E that I gave, but I have no clue on how to do this. I also have no idea on how to get rid of the logarithm.