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
Recommended Citation
Dobson, D., Santosa, F., Shipman, S., & Weinstein, M. (2013). Resonances of a potential well with a thick barrier. SIAM Journal on Applied Mathematics, 73 (4), 1489-1512. https://doi.org/10.1137/120883694