Numerical methods for solving radial Schrödinger equations

摘要

An algorithm previously introduced by Brown et al.(1963) for solving radial Schrödinger equations is revisited and implemented in a more accurate way. The method is firstly applied to equations where potentials are present which are finite at the origin and which have an asymptotic behaviour V(r → 0 as r → ∞. Typical examples of potentials belonging to that class are the Woods-Saxon and the Morse potential. Furthermore the method is also used for Coulomb-like potentials such as the Hulthén and the Hellmann potential. A comparison between the approximated numerical values and other available numerical and exact bound state energies is made.