Hidden symmetry of the 16D oscillator and its 9D coulomb analogue-Reference-Cited by-同舟云学术

Hidden symmetry of the 16D oscillator and its 9D coulomb analogue

Published:2020-07-08 Issue:2 Volume:56 Page:206-216
ISSN:2524-2415
Container-title:Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series
language:
Short-container-title:Vescì Akademìì navuk Belarusì. Seryâ fizika-matematyčnyh navuk

Author:

Lavrenov А. N.¹^ORCID,Lavrenov I. А.²^ORCID

Affiliation:

1. Belarusian State Pedagogical University named after Maxim Tank

2. Octonion Technology Ltd.

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.

Publisher

Publishing House Belorusskaya Nauka

Subject

Computational Theory and Mathematics,General Physics and Astronomy,General Mathematics

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