Application of continued fractions to bound state and scattering problems

The logarithmic derivative of the wavefunction has been put in the form of an infinite continued fraction by the repeated use of successive differentiations of the Schrodinger equation. The eigenvalues and eigenfunctions for bound states have been obtained either by terminating or by a suitable procedure of summing the infinite continued fraction. Various examples have been considered. For scattering problems the relevant Jost function has been calculated from the various convergents of the continued fraction. The resemblance of the procedure to the Pade approximants has been noted. Results on phase-shift calculation have been compared with those obtained by other means.