Carry out the integration ψ = ∫[M(dr/r2)] / √(2m(E-U(r)) - (M2/r2))
E = energy, U = potential, M = angular momentum
using the substitution: u = 1/r for U = -α/r
The Attempt at a Solution
This is as far as I've gotten: -∫ (Mdu) / √(2m(E + αu) - (M2u2))
I have no idea how to take this integral by hand which seems to be what the question is implying. Wolfram gives me something crazy looking.
My book gives the answer as ψ = arccos( (M/r - mα/M) / √(2mE + m2α2/M2) ) ???