# Ellipsoidal coordinates

1. Nov 25, 2008

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$$\theta$$ 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 =]