A New Nonrelativistic Atomic Energy Spectrum of Energy Dependent Potential for Heavy Quarkouniom in Noncommutative Spaces and Phases Symmetries (original) (raw)

A New Nonrelativistic Investigation for Spectra of Heavy Quarkonia with Modified Cornell Potential: Noncommutative Three Dimensional Space and Phase Space Solutions

Journal of Nano- and Electronic Physics

In this paper, we present a further investigation for the exact solvability of non-relativistic quantum spectrum systems for modified Cornell potential (m.c.p.) by means Boopp's shift method instead to solving deformed Schrödinger equation (d.s.e.) with star product, in the framework of both noncommutativity three dimensional real space and space phase (NC: 3D-RSP). The exact corrections for lowest excitations states: ground and first excited states are found straightforwardly for interactions for quarkouniom systems (qq with , ,.. q c b ) by means of the standard perturbation theory. Furthermore, the obtained corrections of energies are depended on: four infinitesimals parameters (, , ,    ), which are induced by position-position and momentum-momentum noncommutativity, the Cornell potential parameters (,, ab ) and the discreet atomic quantum numbers: (j , l , s and m) and we have also shown that, the usual states in ordinary three dimensional spaces are canceled and has been replaced by new degenerated   2 2 1 Nl  sub-states in the new quantum symmetries of (NC: 3D-RSP). It is shown that the (d.s.e.) for (m.c.p.) has the similar behaviors to the relativistic Dirac equation which the polarities of fermionic particle appear exciplicitly.

Heavy Quarkonia with Cornell potential on Noncommutative space

The effect of noncommutative space, to the second order in θ, on heavy quarkonium spectra is studied within the framework of the nonrelativistic Schrodinger equation with the static Cornell potential. Due to this effect, a singular term 1⁄􀝎􀬷 appears in the potential, which is remedied using a regularization scheme by introducing a cut-off radius on the lower limit of the integrals needed for the perturbation computations. The results are applied to the 1S states of 􀜿􀒧, and it is found that the energy shifts are quadratic in the noncommutative parameter θ. By comparing the results with those from experimental 1S-hyperfine splitting of 􀜿􀒧, we infer an upper limit on θ.

The noncommutative Coulomb potential

2021

In this work, we analyze the noncommutative three-dimensional Coulomb potential problem. For this purpose, we used the KustaanheimoStiefel mapping to write the Schrödinger equation for Coulomb potential in a solvable way. Then, the noncommutative hydrogen-like atoms were treated, and their energy levels were found. In addition, we estimate a bound for the noncommutativity parameter.

Hydrogen Atom Spectrum and the Lamb Shift in Noncommutative QED

Physical Review Letters, 2001

We have calculated the energy levels of the hydrogen atom and as well the Lamb shift within the noncommutative quantum electrodynamics theory. The results show deviations from the usual QED both on the classical and on the quantum levels. On both levels, the deviations depend on the parameter of space/space noncommutativity.

New Nonrelativistic Quarkonium Masses in the Two-Dimensional Space-Phase using Bopp’s shift Method and Standard Perturbation Theory

Journal of Nano- and Electronic Physics, 2017

In present work, the exact analytical bound-state solutions of modified Schrödinger equation (MSE) with modified extended Cornel potential (MECP) have been presented using both Bopp's shift method and standard perturbation theory in the noncommutative two dimensional real space and phase (NC-2D: RSP), we have also constructed the corresponding noncommutative Hamiltonian operator which containing two new terms, the first one is modified Zeeman effect and the second is spin-orbital interaction. The theoretical results show that the automatically appearance for both spin-orbital interaction and modified Zeeman effect leads to the degenerate to energy levels to   2 2 1 l  sub states.

HIP-2009-10/TH Dirac Equation in Noncommutative Space for Hydrogen Atom

2013

We consider the energy levels of a hydrogen-like atom in the framework of θ-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels 2S 1/2, 2P 1/2 and 2P 3/2 is lifted completely, such that new transition channels are allowed. 1