The normalization of the radial functions \(R_{n \ell }(r)\) for the solution of Schrödinger’s equation for the Coulomb potential usually proceeds by appealing to the properties of Associated Laguerre polynomials. In this paper we show how to effect the normalization directly from the overall form of the solution and the recursion relation for its series part. Our approach should be applicable to similar problems, such as the harmonic oscillator, and can serve to offer students an alternate method of establishing fully-normalized wavefunctions without invoking the properties of special functions.
