The WKB method for the quantum mechanical two-Coulomb-center problem

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. © 2017, Pleiades Publishing, Ltd.

Авторы
Hnatich M. 1 , Khmara V.M.2 , Lazur V.Y.3 , Reity O.K.3
Номер выпуска
3
Язык
Английский
Страницы
345-358
Статус
Опубликовано
Том
190
Год
2017
Организации
  • 1 Peoples’ Friendship University of Russia, Moscow, Russian Federation
  • 2 Institute of Physics, Pavol Jozef Šafárik University, Košice, Slovakia
  • 3 Department of Theoretical Physics, Uzhhorod National University, Uzhhorod, Ukraine
Ключевые слова
asymptotic solution; semiclassical approximation; two Coulomb centers; WKB method
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/5614/
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