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Generalized quantum mechanical two-Coulomb-center problem (Demkov problem) |
| A. M. Puchkova, A. V. Kozedubb, E. O. Bodniaa |
a Theoretical Department, Institute of Physics, St. Petersburg State University, Petergof, St.Petersburg 198904, Russia;
b Department of Computational Physics, Faculty of Physics, St. Petersburg State University, Petergof, St.Petersburg 198904, Russia |
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Abstract We present a new exactly solvable quantum problem for which the Schrödinger equation allows for separation of variables in oblate spheroidal coordinates. Namely, this is the quantum mechanical two-Coulomb-center problem for the case of an imaginary intercenter parameter and complex conjugate charges are considered. Since the potential is defined by the two-sheeted mapping whose singularities are concentrated on a circle rather than at separate points, there arise additional possibilities in the choice of boundary conditions. A detailed classification of the various types of boundary-value problems is given. The quasi-radial equation leads to a new type of boundary value problem which has never been considered before. Results of the numerical calculations, which allow conclusions to be drawn about the structure of the energy spectrum, are shown. Possible physical applications are discussed.
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Received: 11 December 2012
Revised: 14 March 2013
Accepted manuscript online:
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PACS:
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03.65.Ge
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(Solutions of wave equations: bound states)
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12.39.Pn
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(Potential models)
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31.15.-p
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(Calculations and mathematical techniques in atomic and molecular physics)
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31.90.+s
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(Other topics in the theory of the electronic structure of atoms and molecules)
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| Fund: Dedicated to the memory of Professor Dr. Yu. N. Demkov (12.04.1926-15.11.2010). |
Corresponding Authors:
A. M. Puchkov, A. V. Kozedub, E. O. Bodni
E-mail: putchkov@yahoo.com; alexey.kozhedub@mail.ru; evgeniya.bodnya@cern.ch
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Cite this article:
A. M. Puchkov, A. V. Kozedub, E. O. Bodnia Generalized quantum mechanical two-Coulomb-center problem (Demkov problem) 2013 Chin. Phys. B 22 090306
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