- #1
Tanja
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Might there be a similarity between Dyson's equation and Heisenberg equation? (It's just a feeling, nothing based on arguments.) Both describe how a system (density matrix or Green's function) behaves in time. Both require knowledge of the intial system at time t=0 and the potential acting on the system.
The Dyson equation:
[tex] G = G_0 + G_0 V G[/tex] usually solved with the iteration steps [tex] G_{j+1} = G_0 + G_0 V G{j}[/tex]
The Heisenberg equation of motion (with the density as the operator):
[tex] \rho = U^{\dag} \rho_0 U{ [\tex] with [tex] U = e^{\frac{-i}{\hbar} H t[\tex] (in the case of a time independent Hamiltonian).
There must be bridge, but I can't find a mathematical transition or a common ground. My knowledge on Green's function is just too limited.
Does anybody has an idea what could lead in the right direction?
The Dyson equation:
[tex] G = G_0 + G_0 V G[/tex] usually solved with the iteration steps [tex] G_{j+1} = G_0 + G_0 V G{j}[/tex]
The Heisenberg equation of motion (with the density as the operator):
[tex] \rho = U^{\dag} \rho_0 U{ [\tex] with [tex] U = e^{\frac{-i}{\hbar} H t[\tex] (in the case of a time independent Hamiltonian).
There must be bridge, but I can't find a mathematical transition or a common ground. My knowledge on Green's function is just too limited.
Does anybody has an idea what could lead in the right direction?