The resonance spectrum of Schrodinger operators with rapidly decaying potentialsстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:Resonances of the one-dimensional Schrodinger operator are investigated, that is, the poles of the analytic continuation of the corresponding scattering matrix. For a certain class of superexponentially decreasing potentials, including the Gaussian potential, the Born approximation is substantiated for the problem of localizing the poles of the scattering matrix. This makes it possible to find an asymptotic law (a quantization rule) for the distribution of these poles. For the first time, using the method developed in the paper, asymptotic formulae for resonances are obtained in the case of potentials with noncompact support.