Green function Definition and 85 Threads

I am trying to understand some introductory material on applications of Green's functions and the book which I am following uses the example of an electric circuit subjected to multiple voltage impulses. This is the Google drive viewing link to the few pages I am referring to: . I had to post...

Honestly, I have no real idea. I know for sure the equation connects the initial state ##|\Psi^N_0>##to a final state ##|\Psi^{N+1}_0>##, ##E## is the energy and ##E^N_0## etc are the energy of the initial state and final state. I also know that these energy are related to conduction band and...

The Wikipedia article on Green's functions says, What would be a really simple physical toy problem that would motivate and explain the concept of advanced Green's functions?

First time in PF, I am sorry if I did not choose the right category. I have been doing theory in condensed matter (mostly numerics) as a PhD but I never got to learn proper quantum field theory (QFT). Aside from a few introductory courses at university, I never learned what is a many-body...

Hi guys! I am trying to derive the Hedin's equations used for GW on my own, and I found this equation, but I cannot really derive it, nor find a source where they explain how this can be derived (they link to other papers that in the end don't show where this is coming from). The equation I am...

As in title: Plugging in the definition is straight forward, I am too lazy to type, I will just quote the book Fetter 1971: Up to here everything is very straight forward, in particular, since we are working on free electron gas, ##E=\hbar \omega## However, I have no idea how to arrive...

Hey :) Firstly I want to thank everyone who takes their time to read through this post and who tries to help me. So the issue is the following: I wrote a python code that creates a Lindbladian, and I wanted to try to calculate the Greens function using the Lehmann representation. For the...

Good afternoon! I am writing with such a problem, I hope to find someone who could help me. I'm almost desperate! So, there is such a thing as the Braess paradox, this is a classic paradox for roads and power grids, and there is also such an article...

Hi everyone. Using the Green function, I want to obtain the density of states of a one-dimensional (linear) lattice. Depending on the problem conditions, we will have an iterative loop with 4,000 data for the energy component and a iteration loop with 2,000 data for the wave number component. In...

A conducting sphere of radius a is made up of 3 different shells, upper part a/2 z -a/2, the middle part -a/2 z a, the lower part -a z -a/2 where the center of the sphere is at the origin. The upper part V and the lower part has -V potentials, while the mid part is grounded. Find the...

could anyone explain why in the page of book this figure is related to hartree-fock? I mean why if t1>t2 we have these possibilities? and why not particle propagate from x2t2 to x3t3 instead x3t3+?

I was wondering if there is a way to deduce the solution of the potential of a charge outside a sphere given by the image method, though Green functions. Because of a Dirichlet condition (GD(R,r')=0), I know that a solution can be written as GD=Go+L, where ∇2L=0. But in order to approach this...

I was read this article(https://engineering.purdue.edu/wcchew/ece604f19/Lecture%20Notes/Lect31.pdf). I was read this paper about Huygens' principle(https://engineering.purdue.edu/wcchew/ece604f19/Lecture%20Notes/Lect31.pdf) Main idea of Huygens' principle is how wave function ##ψ(r)##...

In order to obtain equation (3), I think I have to do the Fourier transform in the x direction: \begin{equation} \tilde{G}(k,y,x_0,y_0) = \int_{- \infty}^{\infty} G(x,y,x_0,y_0) e^{-i k x} dx \end{equation} So I have: \begin{equation} -k ^2 \tilde{G}(k,y,x_0,y_0) + \frac{\partial^2...

My fundamental issue with this exercise is that I don't really know what it means to "show that X is a propagator".. Up until know I encountered only propagators of the from ##\langle 0\vert [\phi(x),\phi(y)] \vert 0\rangle##, which in the end is a transition amplitude and can be interpreted as...

Homework Statement: I do know how to solve the resistance network problem in two dimensions. However, in this problem they want it in 3 dimensions and higher and I don't know how to do that Homework Equations: - In the picture you can see the solution to the two dimensional version

I came across an example of a solution to finding the potential of a charged layer using the Green function (here, pdf). The standard algorithm for finding the Green function by boundary conditions for many problems is understandable: \begin{align*} G_\mathrm{Left} = Ax+ B \\ G_\mathrm{Right} =...

Introducing the spacetime spherical symmetric lattice, I use the following notifications in my program. i - index enumerating the nodes along t-coordinate, j - along the r-coordinate, k - along the theta-coordinate, l - along the phi-coordinate. N_t - the number of nodes along t-coordinate. N_r...

The Feynman propagator: $$D_{F}(x,y) = <0|T\{\phi_{0}(x) \phi_{0}(y)\}|0> $$ is the Green's function of the operator (except maybe for a constant): $$ (\Box + m^2)$$ In other words: $$ (\Box + m^2) D_{F}(x,y) = - i \hbar \delta^{4}(x-y)$$ My question is: Which is the operator that...

Is there anyone here that know and understand the OVGF method who can help me? I have some doubts about it, and there is almost nothing about it in literature.

We want to solve the equation. $$H\Psi = i\hbar\frac{\partial \Psi}{\partial t} $$ (1) If we solve the following equation for G $$(H-i\hbar\frac{\partial }{\partial t})G(t,t_{0}) \Psi(t_{0}) = -i\hbar\delta(t-t_{0})$$ (2) The final solution for our wave function is, $$\Psi(t) =...

Hello, If I have a homgeneous linear differential equation like this one (or any other eq): $$y''(x)-y'(x)=0$$ And they give me these Dirichlet boundary conditions: $$y(0)=y(1)=0$$ Can I transform them into a mixed boundary conditions?: $$y(0)=y'(1)=0$$ I tried solving the equation, derivating...

Homework Statement If the Green's function of the electric field in a system is G(x,x')=e^{-i(x-x')^2} I want to calculate the phase of the electric field at x if the source is uniformly distributed at x'=-\infty to x'=\infty Homework EquationsThe Attempt at a Solution Then, the phase of...

Homework Statement We have long wire with constant charge density that is put inside a grounded metal housing with a shape of cylindrical section (a ≤ r ≤ b and 0 ≤ ϕ ≤ α). We need to find potential inside the box. 2. Homework Equations Δf=-(μ/ε0)*∂^2(r), where μ is linear charge density...

I am trying to normalize 4x4 matrix (g and f are functions): \begin{equation} G=\begin{matrix} (1-g^2) &0& 0& 0&\\ 0& (1+f^2)& (-g^2-f^2)& 0 \\ 0 &(-g^2-f^2)& (1+f^2)& 0 &\\ 0& 0& 0& (1-g^2) \end{matrix} \end{equation} It's a matrix that's in a research paper (which I don't have) which gives...

Hi, I am using Mathematica to calculate density of states and current of the Green's function times self energy in most simple form. I am not sure if I am getting current integral over energy implemented correctly. Shouldnt first current plot be a line with a slope? Below is my code...

Hello, Before I begin, a lot of the math I try to describe in this post is stuff I worked out myself and have scribbled down. If something looks fishy or doesn't make sense, it could very well be totally wrong! Apologies for any confusions in advance. Consider a slab of linear isotropic...

Homework Statement [/B] We are heating a semi-infinite slab with a laser (radius of a stream is ##a##), which presents us with a steady surface heating (at ##z=0##), everywhere else on the surface the slab is isolated. How does the temperature change with time? Look at the limit cases: at ##t...

Suppose we have a differential equation with initial conditions ##y_{0}=y^{\prime}_{0}=0## and we need to solve it using a Green Function. Then we set up our differential equation with the right side "forcing function" as ##\delta(t^{\prime}-t)## (or with ##t^{\prime}## and ##t## switched I'm a...

Hello, I'm taking a course in electrostatics and electrodynamics. We learned about finding a potentional using unique Green functions that are dependent of the geometry of the problem. Specificly on a Dirichlet problem we get the solution: Φ(x)=∫ρ(x')G(x,x')d3x' -...

I am reading Jackson Electrodynamics (section 1.10 in 3rd edition) and he is discussing the Poisson eqn $$\nabla^2 \Phi = -\rho / \epsilon_0$$ defined on some finite volume V, the solution using Greens theorem is $$\Phi (x) = \frac{1}{4 \pi \epsilon_0} \int_V G(x,x') \rho(x')d^3x' +\frac{1}{4...

Homework Statement I need to solve a problem like Jackson 3.18. I need to find potential due to the same configuration but the position of two plates is opposite i.e. Plate at Z=0 contains disc with potential V and plate at Z=0 is grounded. Homework EquationsThe Attempt at a Solution I think...

In the context of a project, I had to solve numerically Poisson equation with cylindrical coordinates. I put here results for z = 0 on a 3D mesh 256x256x256. Below 1 figure representing the final solution (in absolute value) in the case of a galaxy; I use the CGS units for the potential. I...

Hi everybody. I have a (1×N) Green function in MATLAB. I want to use the FFt function for Green function to transform the time domain. Does the FFT command work correctly for Green function using: A=fft(Green function, nfft). Here nfft is the number of transformed points. Is it necessary that...

I have a 1×N Green function in energy domain. I want to use the FFT (fast Fourier transform) for this Green function in MATLAB. But this function is non-periodic. Could you help me about this? How can I change the energy interval to convert Green function as a periodic function?

Hey All, I recently posted this in another area but was suggested to put it here instead. Here is my original post:

Homework Statement Hi all, I'm currently reviewing for a final and would like some help understanding a certain part of this particular problem: Determine the retarded Green's Function for the D'Alembertian operator ##D = \partial_s^2 - \Delta##, where ##\Delta \equiv \nabla \cdot \nabla## ...

Hello, I need to solve the Poisson equation in gravitational case (for galaxy dynamics) with Green's function by applying Fast Fourier Transform. I don't understand the method used for an isolated system from (Hockney & Eastwood 1981); it says : I have 2 questions: * Why we duplicate the...

Hello, i don't understand how i integrate the star equation at the figure. Fot example \int d x_1 \int d x_2 \frac{d^2G}{d x_1} = \int d x_1 \frac{d^2G}{d x_1} \int d x_2 but \int d x_2 x_2|^\epsilon_{-\epsilon}=0 ...sure this is a error, but i don't understand how i find the answer...

Hello everyone: I'm confusing with the construction and application of dyadic green's function. If we are in the ideal resonant system where only certain resonant mode is supported in this space (such as cavity), the Green's function can be constructed by the mode expansion that is: Gij(r,r')...

Hello everyone: This is what I read in a paper, the spontaneous emission rate written by Fermi's Golden Rule is just related to the local transverse electric field. Dose anyone can explain to me what's the meaning of "transverse mode" here? Why the emission is not related to longitudinal...

Homework Statement The problem requires to solve the integration to find ## G(t) ## after ##G(\omega)## is found via Fourier transform. We have G(\omega)= \frac{1}{2\pi}\frac{1}{\omega _{0}^2 - \omega ^2} Homework Equations As mentioned previously, the question asks to find ##G(t)## The...

hi guys, my professor told me in the class that when we would like to determine green function there are two general method i.e using image charge and using orthonormal eigen function. However I don't understand what are the specific differences between them. Anybody can help me? Moreover in the...

Homework Statement Write an expression for the Dirichlet Green's function of the part of the space bounded by two infinite conducting plates parallel each other and separated by distance of d. Use Image charge method Homework Equations G (at z=0) =0, G (at z=d) =0 I guess The Attempt at a...

hi, I need some reading materials on green function for SHO. my instructor provided a GF frequency and wanted us to find the deformation of poles , boundary conditions for the function. I need to know which mathematical background should I have to solve this. any useful material suggestion will...

I know that in the vector potential formulation one can use a scalar Green function (to find the said potential and from then on the electric and magnetic fields), and that this works because the components of the potential are in the same direction as those of the source - i.e. a current in the...

Hello, For generating initial velocities on a N-Body code (modeling galaxy dynamics), I need to solve the Poisson equation with Green's function by applying Fast Fourier Transform. The Fourier analysis being more straightforwardly performed in a periodic system, I use the "zero padding trick"...

Hi everyone. I have a very quick question. Can someone tell me how to compute the energy dimensions of an n-point Green function. Consider for example a \lambda\phi^4 scalar theory. I know that the dimensions of an n-pt Green function are 4-n (or something like that). How do I prove it? Thanks

Homework Statement Show that the explicitly covariant expression: GR(x-y) = θ(x0-y0)δ((\vec{x}-\vec{y})2)/2\pi agrees with the retarded Green function: δ(x0-y0-|\vec{x}-\vec{y}|) / (4\pi|\vec{x}-\vec{y}|) Homework Equations N/A The Attempt at a Solution I know that the...

I am having trouble understanding something that I am sure is very basic. Let's say I have a particle that is hopping on a 1d lattice with a hard wall at x=0 in the presence of some potential - anything, say linear ##H_0=F*i## or Coulomb ##H_0=C/i## where i is the label of the site the particle...