This report is concerned with the asymptotic distribution of resonances in the semiclassical limit of a one-dimensional 2 × 2 semiclassical Schrödinger operator. We fix a real energy E0 and suppose that the first potential V1 has a simple well at this level so that P1 has eigenvalues subject to the Bohr-Sommerfeld quantization rule, whereas the second potential V2 is “non- trapping” so that P2 has only continuous spectrum near this level. In such a situation, resonances are expected to appear near E0 in the lower half complex plane.
Resonances for a system of Schr"odinger operators above an energy-level crossing
Andre Martinez;
2020
Abstract
This report is concerned with the asymptotic distribution of resonances in the semiclassical limit of a one-dimensional 2 × 2 semiclassical Schrödinger operator. We fix a real energy E0 and suppose that the first potential V1 has a simple well at this level so that P1 has eigenvalues subject to the Bohr-Sommerfeld quantization rule, whereas the second potential V2 is “non- trapping” so that P2 has only continuous spectrum near this level. In such a situation, resonances are expected to appear near E0 in the lower half complex plane.File in questo prodotto:
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