Scattering resonances for a two-dimensional potential well with a thick barrier

Junshan Lin, Fadil Santosa

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5 Scopus citations

Abstract

This paper is concerned with the scattering resonances of the Schrödinger operator-Δ+VL in ℝ2. The real valued potential VL is a low energy well surrounded by a barrier with finite thickness proportional to L. We are interested in the resonances that are close to the nondegenerate bound state frequencies associated with the potential that has infinitely thick barrier. In particular, it is shown that the difference between a resonance and the associated bound state frequency decays exponentially as a function of the barrier thickness with a rate of L2e-cL. The analysis leads to a perturbative approach for accurately approximating the near bound-state resonances.

Original languageEnglish (US)
Pages (from-to)1458-1488
Number of pages31
JournalSIAM Journal on Mathematical Analysis
Volume47
Issue number2
DOIs
StatePublished - 2015

Keywords

  • Perturbation analysis
  • Scattering resonances
  • Schrödinger operator

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