Quasiclassical Study of the Quantum Mechanical Two-Coulomb-Centre Problem
1 Department of Theoretical Physics, SAS, Institute of Experimental Physics, Watsonova 47, 040 01 Košice, Slovakia
2 Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Joliot-Curie 6, 141980 Dubna, Moscow Region, Russia
3 Faculty of Science, P. J. Šafárik University, Šrobárova 2, 041 54 Košice, Slovakia
4 Department of Theoretical Physics, Uzhhorod National University, Voloshyna 54, 88000 Uzhhorod, Ukraine
Published online: 9 February 2016
A recurrent scheme for finding the quasiclassical solutions of the onedimensional equation got by the separation of variables from the Schrödinger equation in prolate spheroidal coordinates has been elaborated. By means of this scheme, WKB expansion quasiclassical two-Coulomb-centre wave functions at large distances between the fixed positive charges (nuclei) have been constructed for the entire space of the negative particle (electron). Our method provides simple uniform estimates of the eigenfunctions at arbitrary internuclear distances R, R ≫ 1 included. In contrast to the perturbation theory, the interaction need not be very small in the quasiclassical approximation. Its applicability domain is hence wider. That permits analyzing qualitative laws for the behavior and properties of quantum mechanical systems.
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