Coulomb wave function

Summary

Coulomb wave functions are solutions of the Coulomb wave equation $u'' + \left( 1 - \frac{2\eta}{\rho} - \frac{L(L + 1)}{\rho^2} \right) u = 0$. This equation is the radial part of the Schrödinger equation for a charged particle in the field of a point charge. The regular solution $F_L(\eta, \rho)$ vanishes at $\rho = 0$, and the irregular solution $G_L(\eta, \rho)$ does not. Both are confluent hypergeometric functions in disguise.