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!

A Beautiful Looking Gaussian Integral - Please HELP!

  1. Jul 21, 2008 #1
    I have the following Gaussian Integral:

    [tex] \int_{0}^{\infty}2\pi r\left |{\int_{-l/2}^{l/2}\frac{e^\frac{-r^2}{bH}}{(1+ix)(k^{''} - ik^{'}x)H}}dx\right |^2dr [/tex]


    [tex]H = \frac{1+x^2}{k^{''} - ik^{'}x} - i\frac{x - \zeta}{k^{'}}[/tex]

    Assume any characters not defined are constants.

    I agree it does look fantastic, and I'm currently trying to numerically solve it (duh..). I'm using MATLAB and I run into the problem:
    "Warning: System is inconsistent. Solution does not exist."
    Yet I know a solution exists because I'm looking at an article that solved it numerically.

    Any Hints/Advice?
  2. jcsd
  3. Jul 21, 2008 #2
    whats the article? it doesn't say how they solved it? what notation are you taking for granted as known? for example is the zeta the riemann zeta fn ( i know not likely since it doesn't have arguments ) but yea if you tell em for what values of the constants you're trying to numerically integrate i'll put it into mathematica and tell you what i get.
  4. Jul 21, 2008 #3
    Hey ice109,
    I've attached the article. You'll see the equation on page 1 and 2.
    No it doesn't say how they solved it, they just quote the results.
    For the notation:
    zeta, k'', k' and everything else are just real numbers (constants). Well, for my current purpose they are.

    I'm trying to (in a way) reproduce the results in this paper with my own parameters.
    Ok, I havn't got all the parameters with me now, but tomorrow I'll grab them and post it here.
  5. Jul 21, 2008 #4
    Here are my numbers:

    l = 7e-3
    b = 14.516e-6
    k'' = 11.466e6
    k' = 4.387e6
    zeta is actually given by:
    where z is a vector that varies from 0 to 10e-3, f is 2.51e-3. But you can try solving it for one particular value of z.

    I am curious as too how you will solve this since I need to vary several parameters and obtain different results.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook