1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Physics problems related to green function ?

  1. May 27, 2013 #1
    hello all !

    my teacher told me to do a research on examples of problems that has connection with green function on solving differential equations (with programmed numerical solutions) in my final year project , can you give me such problems to work on as an undergraduate ? , thank you !
     
    Last edited: May 27, 2013
  2. jcsd
  3. May 27, 2013 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Just about any problem governed by Laplace's equation, Del^2 Phi = 0. This equation is used in 2-D elasticity and fluid flow.
     
  4. May 28, 2013 #3
    Try simulating a classical damped, driven harmomic oscillator. I'm assuming you're working with Fourier transforms, yes?
     
  5. May 28, 2013 #4
    yes , how about its connection with quantum mechanics ? , can i do that or is it hard for non physics student ?
     
  6. May 28, 2013 #5
    The Schrödinger equation* is a linear PDE with a ##\nabla^2## in it:

    ##
    \imath \hbar \partial_t \Psi(\mathbf{r},t) = \frac{-\hbar^2}{2m}\nabla^2 \Psi(\mathbf{r},t) + V(\mathbf{r},t) \Psi(\mathbf{r},t)
    ##

    So it can be useful in QM to know Green's functions for the Helmholtz equation, which is closely related to what SteamKing mentioned. Probably the simplest example would be to look up a 1-dimensional "particle in a box" problem. Pick some initial wavefunction ##\Psi(x,0)## and use Green's functions and convolution to find future wavefunctions ##\Psi(x,t)##.

    If you want to really show off, combine this with sudu.ghonge's idea and do the same for a 1-dimensional quantum harmonic oscillator instead of a particle-in-a-box. But it might be a good idea to practice on something other than quantum mechanics because QM is often counterintuitive and hard to visualize.

    * in position representation, if anyone asks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Physics problems related to green function ?
  1. Green functions (Replies: 10)

Loading...