New Nonrelativistic Quarkonium Masses in the Two-Dimensional Space-Phase using Bopp’s shift Method and Standard Perturbation Theory (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, l , s and m) and we have also shown that, the usual states in ordinary three dimensional spaces are canceled and has been replaced by new degenerated   2 2 1 Nl  sub-states in the new quantum symmetries of (NC: 3D-RSP).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.

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

Journal of Nano- and Electronic Physics

The modified theories of noncommutative quantum mechanics have engrossed much attention in the last decade, especially its application to the fundamental three equations: Schrödinger, Klein-Gordon and Dirac equations. In this contextual exploration, we further investigate for modified quadratic Yukawa potential plus Mie-type potential (MIQYM) in the framework of modified nonrelativistic Schrödinger equation (MSE) using generalization of Bopp's shift method and standard perturbation theory instead of using directly the generalized Moyal-Weyl product method, we obtained modified energy eigenvalues and corresponding modified anisotropic Hamiltonian operator in both three dimensional noncommutative space and phase (NC-3D: RSP) symmetries.

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

International Letters of Chemistry, Physics and Astronomy, 2017

In this work, an analytical expression for the nonrelativistic energy spectrum of some diatomic molecules was obtained through the Bopp's shift method in the noncommutative (NC) two-dimensional real space-phase symmetries (NC: 2D-RSP) with a new modified Kratzer-type potential (NMKP) in the framework of two infinitesimal parameters θ and θ due to (space-phase) noncommutativity, by means of the solution of the noncommutative Schrödinger equation. The perturbation property of the spin-orbital Hamiltonian operator and new Zeeman effect of twodimensional system are investigated. We have shown that, the new energy of diatomic molecule is the sum of ordinary energy of modified Kratzer-type potential, in commutative space, and new additive terms due to the contribution of the additive part of the NMKP. We have shown also that, the group symmetry of (NC: 2D-RSP) reduce to new subgroup symmetry of NC two-dimensional real space (NC: 2D-RSP) under new modified Kratzer-type interactions.

A new Nonrelativistic Investigation for Interactions in One-electron Atoms with Modified Vibrational-Rotational Analysis of Supersingular plus Quadratic Potential: Extended Quantum Mechanics

Journal of Nano- and Electronic Physics

In our recent work, three-dimensional modified time-independent Schrödinger equation (MSE) of modified vibrational-rotational analysis of supersingular plus quadratic potential (v.r.a.s.q.) potential was solved using Boopp's shift method instead to apply star product, in the framework of both noncommutativity three dimensional real space and phase (NC: 3D-RSP). Furthermore, the exact correction for ground state and first excited state are found straightforwardly for interactions in one-electron atoms has been solved using standard perturbation theory. Furthermore, the obtained corrections of energies are depended on infinitesimal parameters   ,   and   ,  which are induced by position-position and momentum-momentum noncommutativity, respectively, in addition to the discreet atomic quantum numbers: 1 / 2, 1 / 2, j l s l     and m. Moreover, the usual states in ordinary quantum mechanics for vibrational-rotational analysis of supersingular plus quadratic potential are canceled and has been replaced by new degenerated   2 2 1 l  sub-states in the extended new quantum symmetries of (NC: 3D-RSP).

Quarkonium Spectra in the Framework of NonRelativistic Quark Model

Abstract: Matrix Numerove method is used to solve Schrdinger equation via the non relativistic quark model frame work. We use three types of potentials to get bottomonium mesons spectra as an example of heavy quark systems. By using these potentials the spectra of the quarkonium bound states are compared with experimental observed masses to obtain the best results which are in a gooda agreement with the recently published experimental data.