Green function Definition and 65 Threads

There exists very simple formula for Green function for wave equation: G(t,x,t',x') = \delta (t-t'\pm \frac{|x-x'|}{c})/|x-x'| . I wonder whether there exist similar formula for Green function for Klein-Gordon equation (with mass >0) for any boundary condition.

as a student in physics, i cannot see the usefulness of green function to me, the definition of a green function is ugly and singular we have to deal with functions that are not smooth, e.g., the derivative is not continuous at some point. How these functions can be useful in math and...

In my project, we enconter such kind of bessel's differential equation with stochastic source, like \Phi''+\frac{1+2\nu}{\tau}\Phi'+k^2\Phi=\lambda\psi(\tau) where we use prime to denote the derivative with \tau, \nu and \lambda are real constant parameter. how to get the green...

Hello, I don't fully understand the meaning of Green function, and how one should use it. According to Jackson's "Classical Electrodynamics" - 'the method of images is a physical equivalent of the determination of the appropriate F(x, x') to satisfy the boundary conditions'. Where Green...

Hey folks, I'm trying to find the Green function for the equation -\partial_\mu \partial^\mu \phi = K where K is some source term. Its a 2D problem with the wave confined to a rectangular cavity where the cavity is located at z = 0 and z=a. This tells me that G|_0= G|_a=0 I've pretty...

Hey folks, I'm not really sure which forum to put this question in but I figured this was probably the best as it deals with issues of regularization. I'm reading Miltons 'The Casimir Effect'. In chapter one he derives the Casimir energy for a massless scalar field by employing...

find the eigenfunctions and eigen values of the next equation: d^2y/dx^2+u_n^2y=0 where y(0)=0=y(pi). Now find the green function of the above non-homogeneous equation, i.e: d^2G_{\lambda}(x,a)/dx^2-\lambda G_{\lambda}(x,a)=\delta(x-a) where a is in (0,pi) and lambda doesn't equal the...

I need to find the green function of (\frac{d^2}{dx^2}-k^2)\psi(x)=f(x) s.t it equals zero when x approaches plus and minus ifinity. Now according to my lecturer I first need to solve the homogenoues equation, i.e its solution is: psi(x)=Ae^(kx)+Be^(-kx) and G(x,x')=\sum...

Hey folks! I'm starting with the Lagrangian of a massive scalar field and have found an expression for the expectation value of the energy-momentum tensor. <T_{\mu \nu}>=(\partial_\mu \partial_\nu-\frac{1}{2}(g_{\mu \nu}(\partial_\mu \partial_\nu+m^2))G(x-x') let say I have some Green...

Hey, I am trying to find a GF for the function: y''+\frac{1}{24}y=f(x) The function is bounded by: y(0)=y(\pi)=0 I have followed a math textbook that goes through the exact process for the function: y''+k^2y=f(x) and have found a nice looking general solution...

Homework Statement Hey folks, I need to find a Green function for the equation: y'' +1/4y = f(x) With boundary conditions y(0)=y(pi) = 0 The Attempt at a Solution I tried some combination of solutions that look like sin(kx) and sin(k-pi) and looked at the strum liouville...

Hi, I have a basic ODE: y''(x)+\frac{1}{4}y'(x)=f(x) on 0<x<L With Boundary conditions: y(0)=y(L)=0 For which I would like to construct a Green Function. Rather than just plain ask for help, I'll show you what I've been thinking and maybe someone wiser can help/correct me...

I am demonstrating the mean value theorem, which says that for charge-free space the value of the electrostatic potential at any point is equal to the average of the potential over the surface of any sphere centered on that point. I have already found one way to do this, but would also like to...

Dear PF, Could you tell me what is Green function for bilocal operators? As I understand from its form G(x1y1, x2y2,...)... now the pairs of XY are considered as points instead of single X points as in normal Green function G(x1,x2,x3...). So What do we need it for? Or can it be decomposed...

Hello there, I am glad that I found this forum. Because I have a little bit trouble with theoretical physics. The problem is the Green function in theoretical electrodynamic. I try to understand the difference between the Dirichlet Condition and the Neumann Condition. I understand...