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## Main Question or Discussion Point

Hi

I am trying to understand the role of Green's functions in the analysis of a 1D chain of on-site impurities (with the impurity state potential amplitude proportional to V). This is in the context of a course on condensed matter field theory that I am trying to follow.

Can someone explain me the following equation

[tex]G_{ij} = G_{ij}^{0}(\omega) + G_{i0}^{0}(\omega)\frac{V}{1-VG_{00}^{0}(\omega)}G_{0j}(\omega)[/tex]

Here [itex]G_{ij}^{0}(\omega)[/itex] is a 'free' two point Green's function. Here the indices refer to 'sites' (the impurity potential is an on-site potential).

EDIT -- I understand this is a kind of Dyson equation...trying to figure out the notation though. Appreciate inputs.

I am trying to understand the role of Green's functions in the analysis of a 1D chain of on-site impurities (with the impurity state potential amplitude proportional to V). This is in the context of a course on condensed matter field theory that I am trying to follow.

Can someone explain me the following equation

[tex]G_{ij} = G_{ij}^{0}(\omega) + G_{i0}^{0}(\omega)\frac{V}{1-VG_{00}^{0}(\omega)}G_{0j}(\omega)[/tex]

Here [itex]G_{ij}^{0}(\omega)[/itex] is a 'free' two point Green's function. Here the indices refer to 'sites' (the impurity potential is an on-site potential).

**What is the origin of this equation? How does the [itex]1-VG_{00}^{0}(\omega)[/itex] term appear in the denominator?**EDIT -- I understand this is a kind of Dyson equation...trying to figure out the notation though. Appreciate inputs.