1. Not finding help here? Sign up for a free 30min 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!

Integral from Hell?

  1. Oct 29, 2008 #1
    I'm doing a fourier transform of a gaussian wavepacket, so I can get the momentum representation of the wave... To progress I need to evaluate the following integral:

    Int{exp[-(sigma^2.x^2 + bx)/4k].cos[(tx^2 - cx)/8k]}dx

    with sigma, b,k,t and c all being constants, and the limits being ±infinity.
    Any help would be much appreciated!
  2. jcsd
  3. Oct 29, 2008 #2
    resolve cos into exponentials and complete the square. Do a contour shift (or just pretend i is just a parameter)
  4. Nov 3, 2008 #3
    what does that mean?
  5. Nov 3, 2008 #4
    well, I believe that if you work out the integral, you'll get something like
    [tex]\int_{-\infty}^{\infty} e^{-(a+ib)(x-(c+id))^2} dx =\int_C e^{-(a+ib)z^2} dz[/tex]

    where the contour for z is not the real line but shifted by some c+id. One may then argue that since there are no poles anywhere, we can change the contour back to the real line and get a standard gaussian integral. Of course, usually people (at least for me) just pretend i is a real parameter and crank the integral through.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Integral from Hell?
  1. Optimization from hell (Replies: 1)

  2. Integrals from Hell (Replies: 4)