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Abstract

A theoretical analytical investigation for the exact solvability of non-relativistic quantum spectrum systems, at low energy for modified two-dimensional purely sextic double-well potential (2D-modified sextic DWAO potential) is discussed, by means Bopp's shift method, instead to solving deformed Schrödinger equation with star product, in the framework of both noncommutativite two dimensional real space and phase (NC: 2D-RSP), the exact corrections for lowest excitations are found straightforwardly for interactions in one-electron atoms by means of the standard perturbation theory for three special cases. Furthermore, the obtained corrections of energies are depended on the four infinitesimals 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=1±1/2,s=±1/2,1) and the magnetic quantum number m. We have also → generalized our obtained results to include the other atoms with spin S ≠ 1/2.

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