Spherical wave ($e^{\pm ikr}/r$)

For time dependence $e^{-i\omega t}$, the three-dimensional radial solutions $e^{ikr}/r$ and $e^{-ikr}/r$ describe outgoing and incoming spherical waves away from the origin. Their inverse-radius amplitudes make their flux through spheres independent of radius. They form the asymptotic radial ingredients of partial-wave scattering.