Coulomb Wave Function

Author

Eric W. Weisstein
September 12, 2023

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/CoulombWaveFunction.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/CoulombWaveFunction.html.

©2023 Wolfram Research, Inc. except for portions noted otherwise

Differential equation

(r^2) y''+((r^2)-2 η r-l(l+1))y==0

DSolve[y[r] ((r^2)-2 r η-l[1+l])+(r^2) y''[r]==0,y[r],r]

Identities

(CoulombF[n, h, r])==(CoulombH1[n, h, r])-(CoulombH2[n, h, r])

(CoulombH1[n,h,r]-CoulombH2[n,h,r])/(2I)//FullSimplify

(CoulombF[n, 0, r])==r (SphericalBesselJ[n, r])

CoulombF[n,0,r]