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This article is cited in 4 scientific papers (total in 4 papers)
The WKB method for the quantum mechanical two-Coulomb-center problem
M. Hnaticha, V. M. Khmarab, V. Yu. Lazurc, O. K. Reityc a Peoples' Friendship University of Russia, Moscow, Russia
b Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia
c Department of Physics, Uzhgorod State University, Uzhgorod, Ukraine
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 $R\gg1$. 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.
Keywords:
semiclassical approximation, WKB method, two Coulomb centers, asymptotic solution.
Received: 23.12.2015 Revised: 03.02.2016
Citation:
M. Hnatich, V. M. Khmara, V. Yu. Lazur, O. K. Reity, “The WKB method for the quantum mechanical two-Coulomb-center problem”, TMF, 190:3 (2017), 403–418; Theoret. and Math. Phys., 190:3 (2017), 345–358
Linking options:
https://www.mathnet.ru/eng/tmf9132https://doi.org/10.4213/tmf9132 https://www.mathnet.ru/eng/tmf/v190/i3/p403
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