Stuckelberg particle in external magnetic field. Nonrelativistic approximation. Exact solutions
Статья: Stuckelberg particle in external magnetic field. Nonrelativistic approximation. Exact solutions
Автор: Ovsiyuk E.M., Safronov A.P., Ivashkevich A.V., Semenyuk O.A.
Журнал: Известия Коми научного центра УрО РАН @izvestia-komisc
Статья в выпуске: 5 (57), 2022 года.
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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.
St¨uckelberg particle, non-relativistic approximation, magnetic field, projective operators, exact solutions, bound states
Короткий адрес: https://sciup.org/149141293
IDR: 149141293 | DOI: 10.19110/1994-5655-2022-5-79-88
Список литературы Stuckelberg particle in external magnetic field. Nonrelativistic approximation. Exact solutions
- 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.
- 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. 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.
- Редьков, В.М. Поля частиц в римановом пространстве и группа Лоренца / В.М. Редьков. - Минск: Белорусская наука, 2009. - 486 с.
- 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.
