Atomic Wavefunction Integration Question

[Kestrel]

Hello, I'm writing a program, and while I have a decent understanding of wavefunctions and atomic orbitals, this one appears to be a problem I can't beat.

I'm graphing various properties of atomic orbitals (wavefunction, wavefunction squared, radial probability distribution, and a cross section). I'm trying to find, roughly, the point at which the area under the curve reaches 90% (In otherwords, the integral of the function from 0 to x equals 90% the integral of the function from 0 to infinity). I could, I suppose, have the computer do a Riemann sum and calculate it that way, but I was wondering if there was a simpler way. The math is above me, forgive my ignorance, I'm a senior in high school with a semester of calculus under my belt.

Ideally, there would be a simple factor for each quantum number. For example, if you increase n by 1, the you would just multiply the 90% cutoff by 2, or some such number. Increase l by 1, and you would multiply the 90% cutoff point by 1.4. But I'm sure it's more complicated than that.

Any and all help would be greatly appreciated. If all else fails, I'll do a Riemann sum, but I just don't want to tax the computer any more if there's a simpler way.

Thanks in advance!
Scott

 

[gulsen]

If you have the wavefunction, you (or someone here) can calculate the integral analytically and you can simply search for that value. So, do you have the wavefunction (or at least Schrödinger equation? in it's differential form, for it might be solved)

Just for my curiosity, how are you going to make an inifinite Riemann sum?? Do you know where to cut the sum?