- #1
Denver Dang
- 148
- 1
Homework Statement
Hi...
Don't know if it's actually homework, since it's not, but I hope it's okay to post in here.
I am looking for a paper/website/article of some sort, that might have the derivations of the above mentioned coefficients ?
It's for calculating the figure of merit:
[tex]Z=\frac{\sigma {{S}^{2}}}{\kappa }[/tex]
Homework Equations
The equations if was hoping to maybe find some derivatins of is these three:
[tex]\sigma ={{e}^{2}}\int{d\varepsilon \left( -\frac{\partial {{f}_{0}}}{\partial \varepsilon } \right)\Xi \left( \varepsilon \right)}[/tex]
[tex]S=\frac{e{{k}_{B}}}{\sigma }\int{d\varepsilon \left( -\frac{\partial {{f}_{0}}}{\partial \varepsilon } \right)\Xi \left( \varepsilon \right)}\frac{\varepsilon -\mu }{{{k}_{B}}T}[/tex]
[tex]{{\kappa }_{0}}={{k}_{B}}T\int{d\varepsilon \left( -\frac{\partial {{f}_{0}}}{\partial \varepsilon } \right)\Xi \left( \varepsilon \right)}{{\left[ \frac{\varepsilon -\mu }{{{k}_{B}}T} \right]}^{2}}[/tex]
where:
[tex]\[\Xi =\sum\limits_{\overrightarrow{k}}{{{\overrightarrow{v}}_{\overrightarrow{k}}}{{\overrightarrow{v}}_{\overrightarrow{k}}}{{\tau }_{\overrightarrow{k}}}}\][/tex]
The Attempt at a Solution
Don't know if it is possible to find derivations of these, or somewhat similar, or I have to calculate it myself. But I just wanted to try.
Thanks in advance.
Regards.