Hidden symmetry of the 16D oscillator and its 9D coulomb analogue
https://doi.org/10.29235/1561-2430-2020-56-2-206-216
Abstract
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.
About the Authors
А. N. Lavrenov
Belarusian State Pedagogical University named after Maxim Tank
Belarus
Belarus
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
I. А. Lavrenov
Octonion Technology Ltd.
Belarus
Belarus
Ivan A. Lavrenov – Leading Specialist
25, Ya. Kupala Str., 220030, Minsk
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