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

А. N. Lavrenov; I. А. Lavrenov

doi:10.29235/1561-2430-2020-56-2-206-216

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

А. N. Lavrenov, I. А. Lavrenov

https://doi.org/10.29235/1561-2430-2020-56-2-206-216

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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.

Keywords

quadratic Hahn algebra QH(3), 9D coulomb system, 16D harmonic oscillator, Hurwitz transformation, hidden symmetry, SU(1, 1) ⊕ SU (1, 1)

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Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series

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

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Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series

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

Full Text:

Abstract

Keywords

About the Authors

References

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