Hamiltonians and formal multiple scattering theory

The free particle Green function operator, Go, and the full Green function, G, are given by definition respectively by  

Both IV q and ij have the same eigenvalue Ea and correspond to the solutions which coincide with the free particle state Xa in the remote past or future respectively. 

One can also write this in terms of the Green s functions  

As a matter of fact, we have not made any assumptions about the potentials, and may therefore equally well set V = )Tb V in Eq.(3.20) where each V1 is one of the cell potentials. This works as long as the potentials are non-overlapping, and gives us the equation  

By grouping all terms containing only one cell potential, we can rewrite the equation above in terms of the cell t-matrices  

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