- #1
raul_l
- 105
- 0
Sometimes the dielectric function is defined as the connection between the total electric field in a material and the external field,
[tex]
\mathbf{E}(\mathbf{r},\omega) = \int \epsilon^{-1}(\mathbf{r},\mathbf{r'},\omega) \mathbf{E}_{\text{ext}}(\mathbf{r'},\omega) d \mathbf{r'},
[/tex]
and sometimes as the connection between the total effective potential and the externally applied potential,
[tex]
V_{\text{tot}}(\mathbf{r},\omega) = \int \epsilon^{-1}(\mathbf{r},\mathbf{r'},\omega) V_{\text{ext}}(\mathbf{r'},\omega) d \mathbf{r'}.
[/tex]
I don't see how these two definitions are equivalent.
See, e.g. "etsf.grenoble.cnrs.fr/dp/tutorial/dptutorial.pdf" and "cms.mpi.univie.ac.at/mmars/ThesisJudithHarlChapter2.pdf" .
Could somebody comment on that?
[tex]
\mathbf{E}(\mathbf{r},\omega) = \int \epsilon^{-1}(\mathbf{r},\mathbf{r'},\omega) \mathbf{E}_{\text{ext}}(\mathbf{r'},\omega) d \mathbf{r'},
[/tex]
and sometimes as the connection between the total effective potential and the externally applied potential,
[tex]
V_{\text{tot}}(\mathbf{r},\omega) = \int \epsilon^{-1}(\mathbf{r},\mathbf{r'},\omega) V_{\text{ext}}(\mathbf{r'},\omega) d \mathbf{r'}.
[/tex]
I don't see how these two definitions are equivalent.
See, e.g. "etsf.grenoble.cnrs.fr/dp/tutorial/dptutorial.pdf" and "cms.mpi.univie.ac.at/mmars/ThesisJudithHarlChapter2.pdf" .
Could somebody comment on that?
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