Spherical Bessel functions

Summary

The spherical Bessel functions $j_n$ and $y_n$ are the Bessel functions of half-integer order $n + \frac{1}{2}$, rescaled by $\sqrt{\pi / (2x)}$. They solve the radial part of the Helmholtz equation in spherical coordinates. They are elementary: each is a combination of $\sin x$, $\cos x$ and powers of $x$. They describe waves scattered by a sphere and the radial motion of a free quantum particle.