JWKB method and quasilinearisation

Abstract

The eikonal solution of the radial Schrodinger equation for spherically symmetric potentials is treated by the quasilinearisation technique. The first iteration contains all the terms of the full expansion of the eikonal series obtained by Froman and Froman (1965) but with different coefficients. The strength of the centrifugal potential appropriately modified in each order of approximation is obtained stipulating the proper behaviour of the wavefunction at the origin. It leads to an iterative map which converges very fast due to quadratic convergence of quasilinearisation. The energy eigenvalues for the Coulomb potential are obtained by this technique.