A Novel Exactly Theoretical Solvable of Bound States of the Dirac-Kratzer-Fues Problem with Spin and Pseudo-Spin Symmetry

Abstract

,which induced by position-position noncommutativity, in addition to the discreet nonrelativistic atomic quantum numbers: (and m ) and we have also shown that, the usual relativistic states in ordinary three dimensional spaces are canceled and has been replaced by new degenerated   1 2 2  l sub-states in the extended quantum symmetries (NC: 3D-RS).

The Exact Nonrelativistic Energy Eigenvalues for Modified Inversely Quadratic Yukawa Potential Plus Mie-type Potential

“…jl  , thus every state in usually three dimensional space for (MIQYM) potential will be replace, in (NC-3D: RSP) by   It is important to noticing that these results are excellent agreement with our reference [12]. Furthermore, the appearance of the polarization states of a fermionic particle for (MIQYM) potential indicates the validity of obtained results at very high energy where the two relativistic equations Klein-Gordon and Dirac will be applied, which allowing to apply these results of various Nano-particles at Nanoscales.…”

“…On based to the work of the author B.I. Ita [9] to the case of the noncommutative space and space phase in addition to the our previously works [11][12][13][14][15][16][17][18][19][20][21][22][23]. It is worth to mentioning that the (CCRs) will be changes in noncommutative three dimensional spaces and phases to the new canonical commutations relations (NCCRs), in both Schrödinger (SP) and Heisenberg (HP) pictures, as follows [7][8][9][10][11]: J. NANO-ELECTRON.…”

“…PHYS. 9, 02017 (2017) 02017- 2            ˆˆˆˆ, , , and ,ˆˆ, , , and ˆ, ij i j ij i j ij i j i j ij i j ij ij ij x p i x x i p p i x t p t i x t x t i p t p t i                                               [12]:…”

“…Here   in (HP) are determined from two corresponding operators ˆi x and ˆi p in (SP) from the projection relations, respectively [12][13][14]:…”

“…The formalism of star product, Bopp's shift method and the Seiberg-Witten map were played crucial roles in this new theory. The Bopp's shift method will be apply in this paper instead of solving the Schrödinger equation in (NC-3D:RSP) with star product, the Schrödinger equation will be treated by using directly the two new commutators, in addition to usual commutator on quantum mechanics, in the both Schrödinger and Heisenberg representations [12][13][14]:…”