vestifmИзвестия Национальной академии наук Беларуси. Серия физико-математических наукProceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series1561-24302524-2415The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-2430-2020-56-2-206-216vestifm-522Research ArticleФИЗИКАPHYSICSСкрытая симметрия 16D осциллятора и его 9D кулоновского аналогаHidden symmetry of the 16D oscillator and its 9D coulomb analoguehttps://orcid.org/0000-0001-7384-3621ЛаврёновА. Н.LavrenovА. N.

Лаврёнов Александр Николаевич – кандидат физико-математических наук, доцент, доцент кафедры информационных технологий в образовании

ул. Советская, 18, 220030, г. Минск

Alexandre N. Lavrenov – Ph. D. (Physics and Mathematics), Assistant Professor, Assistant Professor of the Department of the Chair of Information Technologies in Education

18, Sovetskaya Str., 220050, Minsk

lanin0777@mail.ruhttps://orcid.org/0000-0002-3650-8987ЛаврёновИ. А.LavrenovI. А.

Лаврёнов Иван Александрович – ведущий специалист

ул. Я. Купалы, 25, 220030, г. Минск

Ivan A. Lavrenov – Leading Specialist

25, Ya. Kupala Str., 220030, Minsk

lanin99@mail.ruБелорусский государственный педагогический университетBelarusian State Pedagogical University named after Maxim TankООО «Октонион технолоджи»Octonion Technology Ltd.202008072020562206216Copyright © Лаврёнов А.Н., Лаврёнов И.А., 20202020Лаврёнов А.Н., Лаврёнов И.А.Lavrenov А.N., Lavrenov I.А.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestifm.belnauka.by/jour/article/view/522

Представлена квадратичная алгебра Хана QH(3) как алгебра скрытой симметрии для определенного класса точно решаемых потенциалов, обобщающих соответственно 16D осциллятор и его по отношению к преобразованию Гурвица 9D кулоновский аналог на основе SU (1,1)⊕ SU (1,1)  . Обсуждается разрешимость уравнения Шредингера для этих задач методом разделения переменных в сферических и параболических (цилиндрических) координатах. Показано, что коэффициенты перекрытия между волновыми функциями в этих координатах совпадают с коэффициентами Клебша – Гордана для SU(1,1) алгебры.

We present the quadratic Hahn algebra QH(3) as an algebra of the hidden symmetry for a certain class of exactly solvable potentials, generalizing the 16D oscillator and its 9D coulomb analogue to the generalized version of the Hurwitz transformation based on SU (1,1)⊕ SU (1,1)  . The solvability of the Schrodinger equation of these problems by the variables separation method are discussed in spherical and parabolic (cylindrical) coordinates. The overlap coefficients between wave functions in these coordinates are shown to coincide with the Clebsch – Gordan coefficients for the SU(1,1) algebra.

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The authors declare that there are no conflicts of interest present.