Generalized quantum mechanical two-Coulomb-center problem (Demkov problem)

doi:10.1088/1674-1056/22/9/090306

中国物理B ›› 2013, Vol. 22 ›› Issue (9): 90306-090306.doi: 10.1088/1674-1056/22/9/090306

Generalized quantum mechanical two-Coulomb-center problem (Demkov problem)

A. M. Puchkov^a, A. V. Kozedub^b, E. O. Bodnia^a

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

收稿日期:2012-12-11 修回日期:2013-03-14 出版日期:2013-07-26 发布日期:2013-07-26
基金资助:
Dedicated to the memory of Professor Dr. Yu. N. Demkov (12.04.1926-15.11.2010).

Generalized quantum mechanical two-Coulomb-center problem (Demkov problem)

A. M. Puchkov^a, A. V. Kozedub^b, E. O. Bodnia^a

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

Received:2012-12-11 Revised:2013-03-14 Online:2013-07-26 Published:2013-07-26
Contact: A. M. Puchkov, A. V. Kozedub, E. O. Bodni E-mail:putchkov@yahoo.com; alexey.kozhedub@mail.ru; evgeniya.bodnya@cern.ch
Supported by:
Dedicated to the memory of Professor Dr. Yu. N. Demkov (12.04.1926-15.11.2010).

摘要/Abstract

摘要： 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.

关键词: two-Coulomb-center problem, potential models

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.

Key words: two-Coulomb-center problem, potential models

中图分类号: (Solutions of wave equations: bound states)

03.65.Ge

12.39.Pn (Potential models) 31.15.-p (Calculations and mathematical techniques in atomic and molecular physics) 31.90.+s (Other topics in the theory of the electronic structure of atoms and molecules)

A. M. Puchkov, A. V. Kozedub, E. O. Bodnia. Generalized quantum mechanical two-Coulomb-center problem (Demkov problem)[J]. 中国物理B, 2013, 22(9): 90306-090306.

A. M. Puchkov, A. V. Kozedub, E. O. Bodnia. Generalized quantum mechanical two-Coulomb-center problem (Demkov problem)[J]. Chin. Phys. B, 2013, 22(9): 90306-090306.

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Generalized quantum mechanical two-Coulomb-center problem (Demkov problem)

Generalized quantum mechanical two-Coulomb-center problem (Demkov problem)

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