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Title: | The WKB method for the quantum mechanical two-Coulomb-center problem |
Authors: | Гнатіч, Міхал Хмара, Віктор Михайлович Лазур, Володимир Юрійович Рейтій, Олександр Костянтинович |
Keywords: | semiclassical approximation, WKB method, two Coulomb centers, asymptotic solution |
Issue Date: | 1-Mar-2017 |
Publisher: | Springer Science+Business Media, Inc. |
Citation: | Hnatich M., Khmara V.M., Lazur V.Y., Reity O.K. // Theor. Math. Phys. - 2017. - V. 190, No 3. - P. 345-358. |
Abstract: | Using a modified perturbation theory, we obtain asymptotic expressions for the two-center quasiradial and quasiangular wave functions for large internuclear distances R. We show that in each order of 1/R, corrections to the wave functions are expressed in terms of a finite number of Coulomb functions with a modified charge. We derive simple analytic expressions for the first, second, and third corrections. We develop a consistent scheme for obtaining WKB expansions for solutions of the quasiangular equation in the quantum mechanical two-Coulomb-center problem. In the framework of this scheme, we construct semiclassical two-center wave functions for large distances between fixed positively charged particles (nuclei) for the entire space of motion of a negatively charged particle (electron). The method ensures simple uniform estimates for eigenfunctions at arbitrary large internuclear distances R, including R >> 1. In contrast to perturbation theory, the semiclassical approximation is not related to the smallness of the interaction and hence has a wider applicability domain, which permits investigating qualitative laws for the behavior and properties of quantum mechanical systems. |
Type: | Text |
Publication type: | Стаття |
URI: | https://dspace.uzhnu.edu.ua/jspui/handle/lib/16488 |
Appears in Collections: | Наукові публікації кафедри диференціальних рівнянь та математичної фізики |
Files in This Item:
File | Description | Size | Format | |
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TMP_2017.pdf | Основна стаття | 488.55 kB | Adobe PDF | View/Open |
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