Мақаланы E-mail арқылы жіберу Runge–Lenz Operator in the Momentum Space
- Авторлар: Efimov S.1
-
Мекемелер:
- Bauman Moscow State Technical University, 105005, Moscow, Russia
- Шығарылым: Том 117, № 9-10 (5) (2023)
- Беттер: 712-716
- Бөлім: Articles
- URL: https://journals.rcsi.science/0370-274X/article/view/145212
- DOI: https://doi.org/10.31857/S1234567823090124
- EDN: https://elibrary.ru/BPSOMB
- ID: 145212
Дәйексөз келтіру
Ашық рұқсат
Рұқсат берілді
Тек жазылушылар үшін
Аннотация
The fundamental quantum Coulomb problem in the momentum space is considered. A differential equation with SO(4) symmetry has been obtained in the momentum space instead of the integral Fock equation. The corresponding equation in the coordinate space is the sum of the squares of the angular momentum and Runge–Lenz operators. This approach is unknown in the momentum space where the Runge–Lenz operator is not applied. The Runge–Lenz operator obtained in the momentum space is simpler than that in the coordinate space and allows one to effectively consider the Coulomb problem in the momentum space. A relation of new operator to the infinitesimal rotation operator of the three-dimensional Fock sphere has been determined.
Авторлар туралы
S. Efimov
Bauman Moscow State Technical University, 105005, Moscow, Russia
Хат алмасуға жауапты Автор.
Email: serg.efimo2012@yandex.ru
Әдебиет тізімі
- Л. Д. Ландау, Е. М. Лифшиц, Квантовая механика: нерелятивисткая теория, Наука, M. (1974)
- L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Nonrelativistic Theory, Pergamon, Oxford (1958).
- H. A. Bethe and E. E. Salpeter, Quantum mechanics of one and two-electron atoms, Springer, Berlin (1957).
- А. И. Базь, Я. Б. Зельдович, А. М. Переломов, Рассеяние, реакции и распады в нерелятивисткой квантовой механике, Наука, M. (1971)
- A. I. Baz, Ya. B. Zel'dovich, and A. M. Perelomov, Scattering, reactions and decays in nonrelativistic quantum mechanics, Israel program for scienti c translations, Jerusalem (1969).
- J. L. Basdevant and J. Dalibard, The Quantum Mechanics Solver, Springer-Verlag, Berlin, N.Y., Heidelberg (2000).
- С. П. Аллилуев, ЖЭТФ 33, 200 (1957).
- А. М. Переломов, В. С. Попов, ЖЭТФ 50, 179 (1966).
- M. Bander, C. Itzykson, Rev. Mod. Phys. 38, 330 (1966).
- В. А. Фок, Начала квантовой механики, Кубуч, Л. (1932); 2-изд., Наука, М. (1976).
- V. A. Fock, Zs. f. Phys. 98, 145 (1935); doi.org/10.1007/BF01336904.
- V. A. Fock, Selected Works: Quantum Mechanics and Quantum Field Theory, Taylor & Francis, CRC Press, Boca Raton, London, N.Y. (2004).
- L. Hulthen, Zs. f. Phys. 86, 21 (1933); doi.org/10.1007/BF013401795.
- B. Casselman, Stereographic Projection, AMS: Feature column (2014); www.ams.org/publiccourreach/..-2014-02-2015.
- S. P. E mov, Theor. Math. Phys. 39, 425 (1979).
- C. П. Ефимов, УФН 192(9), 1019; https://Doi.org/10.3367/UFNr.2021.04.038966.
- A. U. Klimuk and N. Y. Vilenkin, Representation of Lie Groups and Special Functions, Springer, Berlin, Heidelberg (1995).
