| We have demonstrated that using asymptotic expansions and our asymptotic shooting method we can calculate asymptotic connection coefficients for ODE's with high accuracy. Using unified methods we have used these coefficients for accurate calculations of eigenenergies of bound states problems, resonances of quasibound state problems, and phase shifts of scattering problems, where the problems are defined by the appropriate Schrodinger equation. In our calculations we have achieved unprecedented 30S accuracy.;Also by using the asymptotic connection coefficients we have proved a new theorem on the asymptotic zeros of oscillating functions which are solutions of a second order linear differential equation.;In particular, we have calculated eigenenergies of the Debye and the quartic oscillator potential, resonances of Bain's potential, phase shifts for electron scattering from the static potential of hydrogen and phase shifts for elastic scattering of positrons by ground state hydrogen atoms in the 1s-2s close coupling approximation. |
