Green's function Definition and 213 Threads

Griffiths develops an intelgral equation for Scrödinger equation in his QM book. As doing so, he requires Green's function for Helmholtz equation (k^2 + \nabla^2) G( \mathbf r) = \delta^3(\mathbf r) A rigourious series of steps, including Fourier transforms and residue integrals follow...

How does the method of images work? I can see why it works (by going back to the form of the Green function and differentiating) but don't see how useful it is to solve problems. At the moment I am basically memorising the different images for each boundary condition which I am sure is not the...

Homework Statement Consider \nabla ^2 u = Q\left( {x,y,z} \right) in the half space region z > 0 where u(x,y,o) = 0. The relevant Green's function is G(x,y,z|x',y',z'). Find the solution to the PDE in terms of G. If Q\left( {x,y,z} \right) = x^2 e^{ - z} \delta \left( {x - 2}...

Okey Dokey, so I'm bored and decided to play around with some math. I've got a problem that I can't figure out now; I have the green's function for the laplacian G(\vec{x}, \vec{x'}) = - \frac{1}{4\pi |\vec{x} - \vec{x'}|} There are no boundary conditions. Is there any lazy way to figure out...

Homework Statement The homogeneous Helmholtz equation \bigtriangledown^2\psi+\lambda^2\psi=0 has eigenvalues \lambda^2_i and eigenfunctions \psi_i. Show that the corresponding Green's function that satisfies \bigtriangledown^2 G(\vec{r}_1, \vec{r}_2)+\lambda^2 G(\vec{r}_1...

URGENT - Green's Function Solution to Poisson/Helmholtz equations hey, i have an exam pretty soon and couldn't find any answers/hints on how to do this: 1.How do you express the solution f(x') of the Helmholtz equation in terms of the green function g(x,x') in integral form, with dirichlet...

help about the Nonequilibrium Green's Function in H. Haug and A.-P. Jauho Book Quantum kinetics in transport and Optics of Semiconductors Eq.(4.31) C^r(t,t')=A^<(t,t')B^r(t,t')+A^r(t,t')B^<(t,t')+A^r(t,t')B^r(t,t') I can not derive this equation, my result has a extra term \theta(t-t') i.e...

Question a) Find two linearly independent solutions of t^2x''+tx' - x = 0 b) Calculate Green's Function for the equation t^2x''+tx' - x = 0, and use it to find a particular solution to the following inhomogeneous differential equation. t^2x''+tx'-x = t^4 c) Explain why the global...

anybody can recommend a good introducotry book on "advanced and retarded Green's function" and its application to QM, particularly transport problems. Thanks. :smile:

Hi all...need a little help with this one... I need to find the Green's function for the half space Neumann problem in the domain z>0. i.e. Laplacian u=f in D, du/dn=h on the boundary of D. Any ideas?

I'm wondering if the general method I'm using for getting greens function solutions is wrong, because it's not giving me the right answer. Here's what I do. Starting with a differential equation: a(x) \frac{d^2 y(x)}{dx^2} + b(x) \frac{dy(x)}{dx} +c(x) y(x) = d(x) the green's...

Hi! I encountered the problem that I need to decompose the Green function into a set of eigenfunction. Particularly, I have the free space Green function G(\vec r; \vec r') = \frac {e^{i k | \vec r - \vec r'|} } {4 \pi | \vec r - \vec r'|} and I need to express it into series of...

Hello, I have a question concerning path integrals. I have seen it for the first time in a course "many-particle physics", so if the path integral has a wider use: I don't know anything about it. Please think about that when you anser :smile: . As far as I understood: 1.Green's function...