New Non-relativistic Bound States Solutions for Modified Kratzer Potential in One-electron Atoms (original) (raw)
Related papers
Journal of Nano-and electronic Physics, 2018
The new exact energy eigenvalues for new modified Kratzer-type potentials (NMKP) are calculated for a few typical (N 2 , CO , NO , CH) molecules through the Bopp's shift method in the global quantum group (GQG) of noncommutative three-dimensional real space-phase symmetries (NC: 3D-RSP) in the framework of two infinitesimal parameters and due to (space-phase) noncommutativity, by means of the solution of the noncommutative Schrödinger equation (NCSE). The perturbation property of the spin-orbital Hamiltonian operator and new Zeeman effect of 3D system are investigated and the corresponding energy eigenvalues kp (
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quantum mechanics for vibrational-rotational analysis of supersingular plus quadratic potential are canceled and has been replaced by new degenerated 2 2 1 l sub-states in the extended new quantum symmetries of (NC: 3D-RSP).
Journal of Nano- and Electronic Physics
In this paper, we present a novel theoretical analytical perform further investigation for the exact solvability of relativistic quantum spectrum systems for modified Mie-type potential (m.m.t.) potential is discussed for spin-1/2 particles by means Boopp's shift method instead to solving deformed Dirac equation with star product, in the framework of noncommutativity three dimensional real space (NC: 3D-RS). The exact corrections for excited th n states are found straightforwardly for interactions in one-electron atoms by means of the standard perturbation theory. Furthermore, the obtained corrections of energies are depended on four infinitesimal parameter ,which induced by position-position noncommutativity, in addition to the discreet atomic quantum numbers: 1 / 2, 1 / 2, j l s l and m (the angular momentum quantum number) and we have also shown that, the usual states in ordinary two and three dimensional spaces are canceled and has been replaced by new degenerated 2 2 1 l sub-states in the new quantum symmetries of (NC: 3D-RS) and we have also applied our obtained results to the case of modified Krazer-Futes potential.
International Letters of Chemistry, Physics and Astronomy
In this study, three-dimensional modified time-independent Schrödinger equation of modified vibrational-rotational structure of supersingular plus Coulomb (v.r.s.c) 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). We have obtained the explicit energy eigenvalues for ground state and first excited state for interactions in one-electron atoms. Furthermore, the obtained corrections of energies are depended on infinitesimal parameters (Θ,χ) and (θ,σ) which are induced by position-position and momentum-momentum noncommutativity, respectively, in addition to the discreet atomic quantum numbers: j=l±1/2,s=±1/2,l and the angular momentum quantum number m. We have also shown that, the usual states in ordinary three dimensional spaces for ordinary vibrational-rotational structure of supersingular plus Coulomb potential are canceled and has been replaced by new degenerat...
Journal of Nanomedicine Research
The bound-state solutions of the modified Dirac equation (m.d.e.) for the modified anharmonic oscillator (m.a.o.) are presented exactly for arbitrary spin-orbit quantum number () k k by means Bopp's shift method instead to solving (m.d.e.) with star product, in the framework of noncommutativity three dimensional real space (NC: 3D-RS). The exact corrections for th n excited states are found straightforwardly for interactions in one-electron atoms by applying the standard perturbation theory. Furthermore, the obtained corrections of energies are depended on two infinitesimal Investigations on the Relativistic Interactions in One-Electron Atoms with Modified Anharmonic Oscillator 2/12
Int J Quantum Chem, 2000
ABSTRACT In this article exact solutions of a two-electron Schroedinger equation for the Coulomb potential were extended to the Fues-Kratzer-type potential: ({cflx Z}(Ω)/r) + ({cflx A}/r²). The wave function Ψ(r, Ω) is expanded into generalized Laguerre polynomials and hyperspherical harmonics. An analytical expression of two-electron systems is given for matrix elements and accurate energy eigenvalues of the excited state of {sup 1,3}S helium are calculated by using the hyperspherical harmonics method. The present results are compared with previous theoretical calculations and it is concluded that the convergence of energy eigenvalues is faster.
International Frontier Science Letters
A new theoretical analytical investigation for the exact solvability of non-relativistic quantum spectrum systems at low energy for modified inverse power potential (m.i.p.) is discussed by means Boopp’s shift method instead to solving deformed Schrödinger equation with star product, in the framework of both noncommutativite two dimensional real space and phase (NC: 2D-RSP), the exact corrections for lowest excitations are found straightforwardly for interactions in one-electron atoms, muonic, hadronic and Rydberg atoms by means of the standard perturbation theory. Furthermore, the obtained corrections of energies are depended on the four infinitesimals parameters (θ,χ) and (θ,σ), which are induced by position-position and momentum-momentum noncommutativity, in addition to the discreet atomic quantum numbers (j=l±1/1,s=±1/2 andm) and we have also shown that, the old states are canceled and has been replaced by new degenerated 4(2l+1) sub-states.
2018
In this paper, we present further results of our in vestigation for the exact solvability of relativist ic quantum systems with modified pseudo-harmonic (M.P.H.) potential for spi n-1/2 particles by of means Bopp’s shift method ins tead of solving deformed Dirac equation with star product, in the f ramework of noncommutative 3-dimensional real space (NC: 3D-RS) symmetries. The exact corrections for excited th n states are found straightforwardly for interaction s i one-electron atoms by means of the standard perturbation theory. Furth ermore, the obtained corrections of energies are de pended on two infinitesimal parameter Θ andχ which are induced by position-position noncommutati vity, in addition to the discreet
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.