RESONANCES OF A POTENTIAL WELL WITH A THICK BARRIER

Abstract. This work is motivated by the desire to develop a method that allows for easy and accurate calculation of complex resonances of a one-dimensional Schrödinger’s equation whose poten-tial is a low-energy well surrounded by a thick barrier. The resonance is calculated as a perturbation of the bound state associated with a barrier of infinite thickness. We show that the corrector to the bound state energy is exponentially small in the barrier thickness. A simple computational strategy that exploits this smallness is devised and numerically verified to be very accurate. We also provide a study of high-frequency resonances and show how they can be approximated. Numerical examples are given to illustrate the main ideas in this work. Key words. Resonances for Schrödinger’s equation, asymptotic analysis of resonances, approx-imate methods for calculating resonances AMS subject classifications. 35Pxx, 24L16, 65L15 1. Introduction. Resonance