Hey folks,(adsbygoogle = window.adsbygoogle || []).push({});

I'm trying to find the Green function for the equation

[tex]-\partial_\mu \partial^\mu \phi = K[/tex]

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 [tex]G|_0= G|_a=0[/tex]

I've pretty much solved this problem for the case of NO boundary conditions, eg an infinte wave, I'm just stuck on where to put in info on the BC's.

I am confident I have derived the following expression correctly as it matches with a book I am using:

[tex](-\partial_z^2-\lambda^2)g(z,z')=\delta(z-z')[/tex]

where [tex]\lambda^2=\omega^2-k^2 [/tex]

So really this is the problem I need to solve - where g is the reduced Greens function.

I can solve this by taking the FT and using contour integrals...pretty standard, but this is for an infinite wave. My question is 'where and how do I impose boundary conditions for g(0,z')=g(a,z')=0 ??'.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Green Function and Boundary Conditions

Loading...

Similar Threads - Green Function Boundary | Date |
---|---|

A Applying boundary conditions on an almost spherical body | Feb 15, 2018 |

I A question about boundary conditions in Green's functions | Dec 20, 2016 |

Q about Poisson eqn w/ Neumann boundary conditions as in Jackson | Sep 26, 2015 |

Boundary Value Problem + Green's Function | May 30, 2010 |

Green's function for Poisson equation in a box with both mixed boundary conditions | May 22, 2009 |

**Physics Forums - The Fusion of Science and Community**