Dichotomy of WKB-solutions of discrete Schrodinger equationстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:The asymptotic behavior of solutions of a discrete Schrodinger equation is studied via the perturbation theory approach and by the method based on the reduction to the Riccati equation. Solutions of WKB type are constructed which exhibit a dichotomy property similar to that known for differential equations. Provided that the potential is regularly varying in a certain sense, these solutions can be asymptotically represented as products of continued fraction approximants related to the corresponding Riccati equation.