Developers:Dielectric function
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This is based on G. F. Bertsch et al. Phys. Rev. B 62, 7998 (2000).
For the moment we will only consider the terms of the Lagrangean with
.
Contents |
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Standard formulation
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Equation of motion for
Finally:
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The coupling with the TDKS equation
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Exponential formulation
We define
so the Langrangean reads
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Equation of motion for
We will not consider the last two terms, as in the original Lagrangean this term doesn't depend on A, so its contributions will vanish.
Finally:
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Change of variables
What happens if we consider an actual change of variables
?
We are actually back in the Coulomb gauge, where the induced electric field is given by the dipole.
The TDKS equation would be:
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Notation
- Greek superscript indexes: spatial coordinates with implicit sum.
-
: cell volume
-
: number of electrons

