The WKB method for the quantum mechanical two-Coulomb-center problem |
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Authors: | M Hnatich V M Khmara V Yu Lazur O K Reity |
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Institution: | 1.Peoples’ Friendship University of Russia,Moscow,Russia;2.Institute of Physics,Pavol Jozef ?afárik University,Ko?ice,Slovakia;3.Department of Theoretical Physics,Uzhhorod National University,Uzhhorod,Ukraine |
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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. |
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