A New Nonrelativistic Investigation for Interactions in One-Electron Atoms With Modified Inverse-Square Potential: Noncommutative Two and Three Dimensional Space Phase Solutions at Planck’s and Nano-Scales

Abstract

In this paper, we present a novel theoretical analytical perform further investigation for the exact solvability of non-relativistic quantum spectrum systems for modified inverse-square potential (m.i.s.) potential is discussed by means Boopp's shift method instead to solving deformed Schrödinger equations with star product, in the framework of both noncommutativity (two -three) dimensional real space and phase (NC: 2D-RSP) and (NC: 3D-RSP). The exact corrections for excited states are found straightforwardly for interactions in oneelectron atoms by means of the standard perturbation theory. Furthermore, the obtained corrections of energies are depended on four infinitesimals parameters ( , ) and ( , ), which are induced by position-position and momentum-momentum noncommutativity, (NC: 2D-RSP) and (NC: 3D-RSP), respectively, in addition to the discreet atomic quantum numbers: and (the angular momentum quantum number) and we have also shown that, the usual states in ordinary two and three dimensional spaces are cancelled and has been replaced by new degenerated substates in the new quantum symmetries of (NC: 2D-RSP) and (NC: 3D-RSP). Keywords:The inverse-square potential; Noncommutative space; Phase; Star product; Boopp's shift method. A New Nonrelativistic Investigation for Interactions in One-Electron Atoms With Modified InverseSquare Potential: Noncommutative Two and Three Dimensional Space Phase Solutions at Planck's and Nano-Scales 2/15Copyright: ©2016 Maireche ( 1 . 5 ) Here denote to the new quantum Hamiltonian operator in the symmetries of (NC: 2D-RSP) and (NC: 3D-RSP). The very small two parameters and (compared to the energy) are elements of two ant symmetric real matrixes and denote to the new star product, which is generalized between two arbitrary functions and to instead of the usual product in in ordinary (two-three) dimensional spaces :. ( 2 ) Where the two covariant derivatives are denotes to the , respectively, and the two following terms [ , ] are induced by (space-space) and (phase-phase) noncommutativityproperties, respectively, a Boopp's shift method can be used, instead of solving any quantum systems by using directly star product and , and , 13 23 12 23 13ˆˆˆ, , , ,ˆˆˆ, , , , ,ˆˆˆˆ, , , , , The study of inverse-square potential has now become a very interest field due to their applications in different fields [1], this work is aimed at obtaining an analytic expression for the eigenenergies of a inverse-square potential in (NC: 2D-RSP) and (NC: 3D-RSP) using the generalization Boopp's shift method based on mentioned formalisms on above equations to discover the new symmetries and a possibility to obtain another applications to this potential in different fields, it is important to notice that, this potential was studied, in ordinary two dimensional spaces, by authors Shi-Hai Dong and Guo-Hua Sun of the Ref. the Schrödinger equation with a Coulomb plus inverse-square potential in D dimensions [1]. The organization scheme of the study is given as follows: In next ...

Effects of Two-Dimensional Noncommutative Theories on Bound States Schrödinger Diatomic Molecules under New Modified Kratzer-Type Interactions

“…We have solved the modified radial Schrödinger equation and obtained the differences in the energy eigenvalues (29) and (34) which are produced automatically by the effects of spin-orbital interaction (10), (29) and (34) (36) which is the equation of a diatomic molecules under the influence of MKP. It should be pointed out that this treatment considers only first order terms in either θ or θ , it's worth to note that the first part presents the Hamiltonian operator in the ordinary quantum mechanics for MKP while the second and the third parts are respectively present the spin-orbital and new Zeeman Hamiltonians operators which are induced automatically by the NC properties of space and phase.…”

“…In this sub-section we apply the same strategy, which we have seen in our previously works [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] …”

Investigations on the Relativistic Interactions in One-Electron Atoms with Modified Yukawa Potential for Spin 1/2 Particles

“…The three-generalized coordinates  by the following relations, as follows [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]: …”

“…which allow us to getting the operator 2 r on NC three dimensional spaces as follows [28][29][30][31][32][33][34]: (10) the coupling 13 …”

“…Furthermore, the new equal-time anti-commutator for fermionic field operators' in NC spaces can be expressed as [28][29][30][31][32][33][34]: …”