Approximate Solutions to the Klein-Fock-Gordon Equation for the Sum of Coulomb and Ring-Shaped-Like Potentials
We consider the quantum mechanical problem of the motion of a spinless charged relativistic particle with mass M, described by the Klein-Fock-Gordon equation with equal scalar Sr→ and vector Vr→ Coulomb plus ring-shaped potentials. It is shown that the system under consideration has both a discrete...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in High Energy Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/1356384 |
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| author | Sh. M. Nagiyev A. I. Ahmadov V. A. Tarverdiyeva |
| author_facet | Sh. M. Nagiyev A. I. Ahmadov V. A. Tarverdiyeva |
| author_sort | Sh. M. Nagiyev |
| collection | DOAJ |
| description | We consider the quantum mechanical problem of the motion of a spinless charged relativistic particle with mass M, described by the Klein-Fock-Gordon equation with equal scalar Sr→ and vector Vr→ Coulomb plus ring-shaped potentials. It is shown that the system under consideration has both a discrete at E<Mc2 and a continuous at E>Mc2 energy spectra. We find the analytical expressions for the corresponding complete wave functions. A dynamical symmetry group SU1,1 for the radial wave equation of motion is constructed. The algebra of generators of this group makes it possible to find energy spectra in a purely algebraic way. It is also shown that relativistic expressions for wave functions, energy spectra, and group generators in the limit c⟶∞ go over into the corresponding expressions for the nonrelativistic problem. |
| format | Article |
| id | doaj-art-8832c839ba15482d8ae7675e101bb817 |
| institution | Kabale University |
| issn | 1687-7357 1687-7365 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in High Energy Physics |
| spelling | doaj-art-8832c839ba15482d8ae7675e101bb8172025-08-20T03:37:38ZengWileyAdvances in High Energy Physics1687-73571687-73652020-01-01202010.1155/2020/13563841356384Approximate Solutions to the Klein-Fock-Gordon Equation for the Sum of Coulomb and Ring-Shaped-Like PotentialsSh. M. Nagiyev0A. I. Ahmadov1V. A. Tarverdiyeva2Institute of Physics, Azerbaijan National Academy of Sciences, H. Javid Avenue, 131, AZ-1143 Baku, AzerbaijanDepartment of Theoretical Physics, Baku State University, Z. Khalilov St. 23, AZ-1148 Baku, AzerbaijanInstitute of Physics, Azerbaijan National Academy of Sciences, H. Javid Avenue, 131, AZ-1143 Baku, AzerbaijanWe consider the quantum mechanical problem of the motion of a spinless charged relativistic particle with mass M, described by the Klein-Fock-Gordon equation with equal scalar Sr→ and vector Vr→ Coulomb plus ring-shaped potentials. It is shown that the system under consideration has both a discrete at E<Mc2 and a continuous at E>Mc2 energy spectra. We find the analytical expressions for the corresponding complete wave functions. A dynamical symmetry group SU1,1 for the radial wave equation of motion is constructed. The algebra of generators of this group makes it possible to find energy spectra in a purely algebraic way. It is also shown that relativistic expressions for wave functions, energy spectra, and group generators in the limit c⟶∞ go over into the corresponding expressions for the nonrelativistic problem.http://dx.doi.org/10.1155/2020/1356384 |
| spellingShingle | Sh. M. Nagiyev A. I. Ahmadov V. A. Tarverdiyeva Approximate Solutions to the Klein-Fock-Gordon Equation for the Sum of Coulomb and Ring-Shaped-Like Potentials Advances in High Energy Physics |
| title | Approximate Solutions to the Klein-Fock-Gordon Equation for the Sum of Coulomb and Ring-Shaped-Like Potentials |
| title_full | Approximate Solutions to the Klein-Fock-Gordon Equation for the Sum of Coulomb and Ring-Shaped-Like Potentials |
| title_fullStr | Approximate Solutions to the Klein-Fock-Gordon Equation for the Sum of Coulomb and Ring-Shaped-Like Potentials |
| title_full_unstemmed | Approximate Solutions to the Klein-Fock-Gordon Equation for the Sum of Coulomb and Ring-Shaped-Like Potentials |
| title_short | Approximate Solutions to the Klein-Fock-Gordon Equation for the Sum of Coulomb and Ring-Shaped-Like Potentials |
| title_sort | approximate solutions to the klein fock gordon equation for the sum of coulomb and ring shaped like potentials |
| url | http://dx.doi.org/10.1155/2020/1356384 |
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