What is the Green inverse function for a given propagator?

[eljose]

given the propagator:

$$G(x,t)=\frac{1}{e^{xt}+1}$$

and knowing that HG(x,t)=d(x-t) with d the "delta" function and H the Hamiltonian,then how could we construct (knowng G(x,t))the Hamiltonian?...

I one work i heard about the Green inverse function, how is it calculated?

 

[marlon]

Well that is quite some work ? Are you expected to do that all on your own ? Normally you should have seen this in your QFT-course or your QM-course. It is an integral equation that you'll need to solve

regards
marlon

 

[dextercioby]

I think you can use Fourier Transforms to find the Forurier transform of the operator you're looking for.

 

[marlon]

I think you can use Fourier Transforms to find the Forurier transform of the operator you're looking for.

Well, that's not all there is to it.

The OP must have seen some analoguous systems in his/her QFT-course, otherwise i really don't see the point of us starting to discuss this topic

marlon

 

[dextercioby]

It's Jose.He's a "he".It doesn't seem like QFT to me...

 

[marlon]

It's Jose.He's a "he".It doesn't seem like QFT to me...

it has to be QM or QFT, you cannot tell which one based upon these data

marlon

 

[reilly]

Try setting 1+exp(xt) = z. Then G=1/z, and work backwards from Poisson's Eq in z.

Regards,
Reilly Atkinson