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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

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    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.
     
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