New Bound States for Modified Vibrational-Rotational Structure of Supersingular Plus Coulomb Potential of the Schrödinger Equation in One-Electron Atoms

Maireche, Abdelmadjid

doi:10.18052/www.scipress.com/ILCPA.73.31

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New Bound States for Modified Vibrational-Rotational Structure of Supersingular Plus Coulomb Potential of the Schrödinger Equation in One-Electron Atoms

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Abstract:

In this study, three-dimensional modified time-independent Schrödinger equation of modified vibrational-rotational structure of supersingular plus Coulomb (v.r.s.c) potential was solved using Boopp’s shift method instead to apply star product, in the framework of both noncommutativity three dimensional real space and phase (NC: 3D-RSP). We have obtained the explicit energy eigenvalues for ground state and first excited state for interactions in one-electron atoms. Furthermore, the obtained corrections of energies are depended on infinitesimal parameters (Θ,χ) and (θ,σ) which are induced by position-position and momentum-momentum noncommutativity, respectively, in addition to the discreet atomic quantum numbers: j=l±1/2,s=±1/2,l and the angular momentum quantum number m. We have also shown that, the usual states in ordinary three dimensional spaces for ordinary vibrational-rotational structure of supersingular plus Coulomb potential are canceled and has been replaced by new degenerated 2(2l+1) sub-states in the extended new quantum symmetries of (NC: 3D-RSP).

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Periodical:

International Letters of Chemistry, Physics and Astronomy (Volume 73)

Pages:

31-45

DOI:

https://doi.org/10.18052/www.scipress.com/ILCPA.73.31

Citation:

A. Maireche, "New Bound States for Modified Vibrational-Rotational Structure of Supersingular Plus Coulomb Potential of the Schrödinger Equation in One-Electron Atoms", International Letters of Chemistry, Physics and Astronomy, Vol. 73, pp. 31-45, 2017

Online since:

April 2017

Authors:

Abdelmadjid Maireche

Keywords:

Boopp’s Shift Method, Noncommutative Phase, Noncommutative Space, Star Product, Vibrational-Rotational Structure of Supersingular Plus Coulomb Potential

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[3] A. Maireche, "The Klein–Gordon equation with modified Coulomb plus inverse-square potential in the noncommutative three-dimensional space", Modern Physics Letters A, p. 2050015, 2019

DOI: https://doi.org/10.1142/S0217732320500157