Wavefunction expansion in terms of spherical bessel functions

A formalism is derived for expanding the solutions of the Schrödinger equation in terms of spherical Bessel functions. The regular and the irregular solutions are treated. A relation between the expansion coefficients and the phase shifts is derived. As an application, the expansion coefficients of both the irregular and regular Coulomb wavefunctions are given in a form of a simple recurrence relation. The expansions have been checked numerically and found to be very suitable for calculating the regular Coulomb wavefunction in a very large region of the coordinate and the Coulomb parameter.