St¨uckelberg particle in external magnetic field. Nonrelativistic approximation. Exact solutions-Reference-Cited by-同舟云学术

St¨uckelberg particle in external magnetic field. Nonrelativistic approximation. Exact solutions

Published:2022-12-20 Issue:5 Volume:0 Page:79-88
ISSN:1994-5655
Container-title:Proceedings of the Komi Science Centre of the Ural Division of the Russian Academy of Sciences
language:en
Short-container-title:

Author:

Ovsiyuk E.,Safronov A.,Ivashkevich A.,Semenyuk O.

Abstract

The St¨uckelberg equation for a particle with two spin states, S = 1 and S = 0, is studied in the presence of an external uniform magnetic field. In relativistic case, the particle is described by an 11-component wave function. On the solutions of the equation, the operators of energy, the third projection of the total angular momentum, and the third projection of the linear momentum along the direction of the magnetic field are diagonalized. After separation of variables, we derive a system for 11 functions depending on one variable. We perform the nonrelativistic approximation in this system. For this we apply the known method of deriving nonrelativistic equations from relativistic ones, which is based on projective operators related to the matrix Γ0 of the relativistic equation. The nonrelativistic wave function turns out to be 4-dimensional. We derive the system for 4 functions. It is solved in terms of confluent hypergeometric functions. There arise three series of energy levels with corresponding solutions. This result agrees with that obtained for the relativistic St¨uckelberg equation.

Publisher

Komi SC UB RAS

Subject

General Earth and Planetary Sciences,General Energy

Reference5 articles.

1. Ovsiyuk, E.M. St¨uckelberg particle in external magnetic field, and the method of projective operators / E.M. Ovsiyuk, A.P. Safronov, A.V. Ivashkevich, O.A. Semenyuk // Известия Коми НЦ УрО РАН. – 2022. – № 5 (57). – С. 69–78., Ovsiyuk, E.M. St¨uckelberg particle in external magnetic field, and the method of projective operators / E.M. Ovsiyuk, A.P. Safronov, A.V. Ivashkevich, O.A. Semenyuk // Izvestiya Komi NTs Uro RAN [Proc. of the Komi Sci. Centre, Ural Branch, RAS]. – 2022. – № 5 (57). – P. 69–78.

2. Богуш, А.А. Нерелятивистский предел в общековариантной теории векторной частицы / А.А. Богуш, В.В. Кисель, Н.Г. Токаревская, В.М. Редьков // Известия НАН Беларуси. Серия физ.-мат. наук. – 2002. – № 2. – С. 61–66., Bogush, A.A. Nerelyativistskij predel v obshchekovariantnoj teorii vektornoj chasticy [Nonrelativistic approximation in general covariant theory of the vector particle] / A.A. Bogush, V.V. Kisel, N.G. Tokarevskaya, V.M. Red’kov // Vestsі NAN Belarusі. Ser. fіz.-matem. navuk [Proc. NAS of Belarus. Phys. and mathem. ser.]. – 2002. – Vol. 2. – P. 61–66.

3. Bogush, A.A. Duffin-Kemmer-Petiau formalism reexamined: nonrelativistic approximation for spin 0 and spin 1 particles in the Riemannian space-time / A.A. Bogush, V.V. Kisel, N.G. Tokarevskaya, V.M. Red’kov // Annales de la Fondation Louis de Broglie. – 2007. – Vol. 32. – № 2–3. – P. 355–381., Bogush, A.A. Duffin-Kemmer-Petiau formalism reexamined: nonrelativistic approximation for spin 0 and spin 1 particles in the Riemannian space-time / A.A. Bogush, V.V. Kisel, N.G. Tokarevskaya, V.M. Red’kov // Annales de la Fondation Louis de Broglie. – 2007. – Vol. 32. – № 2–3. – P. 355–381.

4. Редьков, В.М. Поля частиц в римановом пространстве и группа Лоренца / В.М. Редьков. – Минск: Белорусская наука, 2009. – 486 с., Red’kov, V.M. Polya chastic v rimanovom prostranstve i gruppa Lorenca [Fields in Riemannian space and the Lorentz group] / V.M. Red’kov. – Minsk: Belorusskaya nauka [Belarusian Science]. – 2009. – 486 p.

5. Ovsiuyk, E.M. St¨uckelberg particle in the Coulomb field, nonrelativistic approximation, wave functions and spectra / E.M. Ovsiyuk, O.A. Semenyuk, A.V. Ivashkevich, M. Neagu // Nonlinear Phenomena in Complex Systems. – 2022. – Vol. 25. – № 3. – P. 352–367., Ovsiuyk, E.M. St¨uckelberg particle in the Coulomb field, nonrelativistic approximation, wave functions and spectra / E.M. Ovsiyuk, O.A. Semenyuk, A.V. Ivashkevich, M. Neagu // Nonlinear Phenomena in Complex Systems. – 2022. – Vol. 25. – № 3. – P. 352–367.

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Stueckelberg particle in the uniform electric field, solutions with cylindrical symmetry;Proceedings of the Komi Science Centre of the Ural Division of the Russian Academy of Sciences;2024-08-07