EFFICIENT, RELIABLE COMPUTATION OF RESONANCES OF THE ONE-DIMENSIONAL SCHRODINGER-EQUATION

We present a numerical method, implemented in a Fortran code RESON, for computing resonances of the radial one-dimensional Schrodinger equation, for an underlying potential that decays sufficiently fast at infinity. The basic approach is to maximize the time-delay function T(lambda) as in the LeRoy program TDELAY. We present some theory that allows a preliminary bracketing of the resonance and various ways of reducing the total work. Together with automatic meshsize selection this leads to a method that has proved efficient, robust, and extremely trouble-free in numerical tests. The code makes use of Marletta's Sturm-Liouville solver, SL02F, due to go into the NAG library. (C) 1994 Academic Press, Inc.