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A Green's function is the impulse response of an inhomogeneous differential equation defined on a domain, with specified initial conditions or boundary conditions, thereby restricting that equation's fundamental solution. In QFT, it is essentially the propagator.
3
votes
Conditions to determine the Green's function for scattering phenomena
"My problem here is the following: to find G we need boundary conditions of the problem. I can't understand, though, what boundary conditions we should impose here.
So to solve scattering prob …
6
votes
How is Lippmann-Schwinger equation derived?
Most of the time, an (elastic) scattering problem can be reduced in :
An incoming initial wave / quantum state $|\phi\rangle$, which most of the time is taken to be a plane wave / free state $|\text …
11
votes
Accepted
How is Green function in many-body theory introduced?
Because these are actually Fourier transform of the usual Green functions.
Consider the Schrödinger equation :
$$
\hat{\mathcal{H}}|\Psi(t)\rangle=\mathrm{i}\partial_t|\Psi(t)\rangle
$$
The general so …
19
votes
What do the poles of a Green function mean, physically?
Let me expand a little more on what Craig Thone just said :
Consider the energy/frequency-dependent Green function :
$$
\tilde{G}(\omega)=\frac{1}{\omega-(a-\mathrm{i}b)}
$$
with one single pole in $ …