Resonances of a potential well with a thick barrier

Document Type

Article

Publication Date

10-8-2013

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 potential 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. © 2013 Society for Industrial and Applied Mathematics.

Publication Source (Journal or Book title)

SIAM Journal on Applied Mathematics

First Page

1489

Last Page

1512

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