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Journal of Nano- and Electronic Physics

Effects of Three-Dimensional Noncommutative Theories on Bound States Schrödinger Molecular under New Modified Kratzer-type Interactions

Abdelmadjid Maireche

Published Jan 1, 2018• 6 citations
Publisher

Abstract

The new exact energy eigenvalues for new modified Kratzer-type potentials (NMKP) are calculated for a few typical (N2, CO, NO, CH) molecules through the Bopp’s shift method in the global quantum group (GQG) of noncommutative three-dimensional real space-phase symmetries (NC: 3D-RSP) in the framework of two infinitesimal parameters  and  due to (space-phase) noncommutativity, by means of the solution of the noncommutative Schrödinger equation (NCSE). The perturbation property of the spin-orbital Hamiltonian operator and new Zeeman effect of 3D system are investigated and the corresponding energy eigenvalues Ekp(n, j ,l ,s ) and nc -kpE (n, j ,l ,s,m) are easily calculated from standard perturbation theory. We have shown also that, the GQG of (NC: 3D-RSP) reduce to new sub-group symmetry of NC threedimensional real space (NC: 3D-RS) under new three-dimensional NMKP interactions.

DOI
10.21272/jnep.10(2).02011

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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.