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Ellipsoidal coordinates

  1. Nov 25, 2008 #1
    When looking at the hydrogen molecular ion H+, you produce solutions in elliptical coordinates, which i found fine, until i came across a problem wheni was testing myself by calculating a 1pz overlap integral: i get a cos2[tex]\theta[/tex] in the integral. Now i have had no problem solving this for 1s, this didnt involved only functions of r, the distance from electron to each nucleus. I am at a loss as how to substitute this away. Basically the equation that needs solving looks like this

    \int_{0}^{2\pi} d\phi \int_{1}^{\infty} d\mu \int_{-1}^{1} d\nu k (\mu^2 - \nu^2)^2 cos^2\theta exp(-\mu R/2a)

    This is for the most part not that hard an integral to solve, just long, messy, with many places to lose a sign. All i can't figure is our pesky friend the cosine. Any suggestions?

    steve =]
  2. jcsd
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