Solving radial wavefunction in odd central potential

[FunkyDwarf]

Hey guys,

I have a question regarding solving a radial wavefunction DE which i have written up in Mathematica and saved as a pdf http://members.iinet.net.au/~housewrk/PFpost.pdf" as I was already doing the work in MM and writing it all up again in LaTeX seemed a bit of a waste of time.

If anything is not clear or wrong or whatever please let me know and i will respond as best i can =D

Cheers
-G

 

[SpectraCat]

Hey guys,

I have a question regarding solving a radial wavefunction DE which i have written up in Mathematica and saved as a pdf http://members.iinet.net.au/~housewrk/PFpost.pdf" as I was already doing the work in MM and writing it all up again in LaTeX seemed a bit of a waste of time.

If anything is not clear or wrong or whatever please let me know and i will respond as best i can =D

Cheers
-G

The math in that document is completely unreadable ... but regardless, can't you use the usual trick of multiplying the radial wavefunction by r (or some other simple function) to wipe out the pole at r=0? What is the form of your central potential? Knowing that might help to analyze the asymptotic limit you are after.

 

[FunkyDwarf]

Yeah sorry, i should have been more mindful of the margins. Like i said, I've tried several function substitutions including that usual trick; i still end up with an r dependence in the denominator for the coefficient of R(r). The form of the central potential is unknown, if i knew that i could probably do some usual wave scattering things. This radial equation was derived from solving the Klein Gordon equation in the interior Schwarzschild metric, so it is 'like' a central gravitational potential, but not in a Newtonian sense.

I have updated that pdf in an attempt to make it more readible, but let's be fair, that equation is a piece of **** to read anyway you write it :)