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Review Article Volume 7 Issue 1
A New Relativistic Bound States Solution for Modified Pseudoharmonic Potential in One-electron Atoms at Planck’s and Nano-Scales
Abdelmadjid Maireche
Received: January 01, 1971 | Published: January 12, 2018
Citation: Maireche A (2018) A New Relativistic Bound States Solution for Modified Pseudoharmonic Potential in One-electron Atoms at Planck’s and Nano-Scales. J Nanomed Res 7(1): 00168. DOI: 10.15406/jnmr.2018.07.00168
Abstract
In this paper, we present solutions of the modified Dirac equation (MDE) with modified pseudoharmonic (MPH) potential for spin-1/2 particles by means Bopp’s shift method, in the framework of noncommutativity 3-dimensional real space (NC: 3D-RS) symmetries. The exact corrections for 
excited states are found straightforwardly by means of the standard perturbation theory. It is found that the energy eigenvalues strongly depend on the potential parameters, two infinitesimal parameter (
and 
), which induced by position-position noncommutativity, in addition to the discreet atomic quantum numbers (
and 
(
) ) and we have also shown that, the usual states in ordinary 3-.dimensions are canceled and has been replaced by new degenerated 
and 
sub-states under the pseudo spin symmetry and spin symmetry conditions, respectively in the new quantum group (NC: 3D-RS).
Keywords: Nano-Scales, Dirac equation, Pseudoharmonic potential, Noncommutative space, Star product, Bopp’s shift method, Commutations, Harmonicpotential, Dimensional, Schrödinger Picture, Bound-state, Quantum system
©2018 Maireche. This is an open access article distributed under the terms of the, which permits unrestricted use, distribution, and build upon your work non-commercially.