This is the Helmholtz equation and can be solved using separation of variables. If spherical coordinates are used to describe a problem, then the solution to the angular part of the Helmholtz equation is given by spherical harmonics, and the radial equation now becomes [ d 2 d r 2 + 2 r d d r + k 2 − − l ( l + 1 ) r 2 ] f l ( r ) = 0.