Numerical Method for Calculating Resonant-State Wave Functions

摘要

An initial-value method of numerical solving of Sturm-Liouville problems is applied to find the solution to the Schroedinger equation which corresponds to a resonance situation. The depth of the nuclear potential is regarded as an eigenvalue, which is obtained by iteration. Having established the nuclear potential, the resonant wavefunction is generated by integrating numerically the Schroedinger differential equation inwards from larger radii using the initial conditions of G(r), where G is the irregular Coulomb function. Because the solution is exactly on resonance, no searching for the phase shift is required. Consequently, the suggested procedure may be employed even if the resonance widths are extremely narrow (e.g., 10 exp -16 MeV). (Atomindex citation 09:397272)