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 language | English (US) |
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Pages (from-to) | 1458-1488 |
Number of pages | 31 |
Journal | SIAM Journal on Mathematical Analysis |
Volume | 47 |
Issue number | 2 |
DOIs | |
State | Published - 2015 |
Bibliographical note
Publisher Copyright:© 2015 Society for Industrial and Applied Mathematics.
Keywords
- Perturbation analysis
- Scattering resonances
- Schrödinger operator