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5. Appendix 1: Proof of
Grand Partition Function:
|
(5.1) |
Let us write the external and internal Boltzmann factors as
|
(5.2) |
Then
|
(5.3) |
Grand Potential:
|
(5.4) |
Varying the external potential according to
we find
|
|
|
(5.5) |
|
|
|
(5.6) |
|
|
|
(5.7) |
|
|
|
(5.8) |
|
|
|
(5.9) |
It follows that
|
(5.10) |
On the other hand,
Therefore
|
(5.12) |
Since
we have
|
(5.13) |
q.e.d.
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1.2
Next: Bibliography
Up: Density Functional Theory for
Previous: 4.3 Outlook
Franz J. Vesely Oct 2001
See also: "Computational Physics - An Introduction," Kluwer-Plenum 2001