Efficient, reliable computation of resonances of the one-dimensional Schrödinger equation (Q1331430)

An algorithm is derived for computing resonances of the one-dimensional Schrödinger equation modelling e.g. the interaction of an electron with a spherically symmetric nucleus. The method is based on the time-delay definition of a resonance as in the program TDELAY by \textit{R. J. LeRoy} [Program No. KQ03, Nat. Resource Comput. Chem., Software Catalog Vol. I (1980)]. By this approach the time-delay function \(\tau(\lambda)\) is maximized. The study is concentrated on the one-barrier case of the potential. Bracketing of the resonance is discussed and an iteration is given to find the bracketing interval. The algorithm is implemented in the code RESON. Numerical tests are shown using the Sturm-Liouville solver SLO2F of \textit{M. Marletta} and \textit{J. D. Pryce} [J. Comput. Appl. Math. 39, No. 1, 57-78 (1992; Zbl 0747.65070)] and are compared for the codes RESON, RESONE, TDELAY, Lennard-Jones, and Morse potentials.