What is the Green inverse function for a given propagator?

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Discussion Overview

The discussion centers around the calculation of the Green inverse function for a given propagator, specifically G(x,t) = 1/(e^(xt) + 1). Participants explore how to construct the Hamiltonian from the propagator and the implications of this relationship in the context of quantum mechanics (QM) and quantum field theory (QFT).

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions how to construct the Hamiltonian given the propagator and mentions the Green inverse function.
  • Another participant suggests that this is typically covered in QFT or QM courses and indicates that it involves solving an integral equation.
  • Some participants propose using Fourier Transforms to find the Fourier transform of the operator in question.
  • There is a suggestion to set 1 + exp(xt) = z to work backwards from Poisson's equation in z.
  • Participants express uncertainty about whether the discussion pertains to QM or QFT, indicating that the information provided is insufficient to determine the context definitively.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the specific context (QM vs. QFT) of the problem, and there are competing views on the methods to approach the calculation of the Green inverse function.

Contextual Notes

There are limitations regarding the assumptions made about the context of the propagator and the Hamiltonian, as well as the mathematical steps involved in the proposed methods, which remain unresolved.

eljose
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given the propagator:

[tex]G(x,t)=\frac{1}{e^{xt}+1}[/tex]

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?
 
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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
 
I think you can use Fourier Transforms to find the Forurier transform of the operator you're looking for.
 
bigubau said:
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
 
It's Jose.He's a "he".It doesn't seem like QFT to me...
 
bigubau said:
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
 
Try setting 1+exp(xt) = z. Then G=1/z, and work backwards from Poisson's Eq in z.

Regards,
Reilly Atkinson
 

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