Open AccessHidden symmetry of the 16D oscillator and its 9D coulomb analogue
Author(s) -
А. N. Lavrenov,
I. А. Lavrenov
Publication year - 2020
Publication title -
vescì nacyânalʹnaj akadèmìì navuk belarusì. seryâ fìzìka-matèmatyčnyh navuk
Language(s) - English
Resource type - Journals
eISSN - 2524-2415
pISSN - 1561-2430
DOI - 10.29235/1561-2430-2020-56-2-206-216
Subject(s) - parabolic coordinates , symmetry (geometry) , quadratic equation , mathematics , wave function , coulomb , mathematical physics , transformation (genetics) , schrödinger equation , separation of variables , algebra over a field , pure mathematics , physics , quantum mechanics , mathematical analysis , generalized coordinates , geometry , partial differential equation , log polar coordinates , biochemistry , chemistry , gene , electron
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.