Resonances of a potential well with a thick barrier

D. C. Dobson, F. Santosa, S. P. Shipman, M. I. Weinstein

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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.

Original languageEnglish (US)
Pages (from-to)1489-1512
Number of pages24
JournalSIAM Journal on Applied Mathematics
Issue number4
StatePublished - Oct 8 2013


  • Approximate methods for calculating resonances
  • Asymptotic analysis of resonances
  • Resonances for Schrödinger's equation

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    Dobson, D. C., Santosa, F., Shipman, S. P., & Weinstein, M. I. (2013). Resonances of a potential well with a thick barrier. SIAM Journal on Applied Mathematics, 73(4), 1489-1512.