New Exact Non-relativistic Energy Eigen Values for Modified Inversely Quadratic Hellmann Plus Inversely Quadratic Potential (original) (raw)
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New Exact Energy Eigen-Values for (Miqyh) and (Miqhm) Central Potentials: Non-Relativistic Solutions
African Review of Physics, 2016
In this paper, we solved modified Schrödinger equat ion (MSE) for two potentials namely: modified inversely qua dr tic Yukawa potential plus inversely quadratic Hellmann potential (MIQYH) and modified inversely quadratic Hellmann plus Mie-type potential ( MIQHM), which are equal to the sum of inversely quadrati c Yukawa potential plus inversely quadratic Hellmann and inversely quadratic Hellmann plus Mietype potential, respectively, using a generalizatio n of Boopp’s shift method and standard perturbation theory instead of using directly star product method. We then obtaine d modified energy eigenvalues and corresponding modified Hamiltonians n both three dimensional non-commutative space an d phase ( NC-3D: RSP).
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.
Ukrainian Journal of Physics, 2020
Within the framework of nonrelativistic noncommutative quantum mechanics using the improved approximation scheme to the centrifugal term for any l-states via the generalized Bopp's shift method and standard perturbation theory, we have obtained the energy eigenvalues of a newly proposed generalized Hellmann potential model (the GHP model) for the hydrogenic atoms and neutral atoms. The potential is a superposition of the attractive Coulomb potential plus Yukawa one, and new central terms appear as a result of the effects of noncommutativity properties of space and phase in the Hellmann potential model. The obtained energy eigenvalues appear as a function of the generalized gamma function, the discrete atomic quantum numbers (, , , and), infinitesimal parameters (, ,) which are induced by the positionposition and phase-phase noncommutativity, and, the dimensional parameters (Θ,) of the GHP model, in the nonrelativistic noncommutative three-dimensional real space phase (NC: 3D-RSP). Furthermore, we have shown that the corresponding Hamiltonian operator with (NC: 3D-RSP) symmetries is the sum of the Hamiltonian operator of the Hellmann potential model and two operators, the first one is the modified spin-orbit interaction, while the second is the modified Zeeman operator for the hydrogenic and neutral atoms.
Journal of Atomic and Molecular Physics, 2013
The solutions to the Schrödinger equation with inversely quadratic Yukawa and inversely quadratic Hellmann (IQYIQH) potential for any angular momentum quantum number have been presented using the Nikiforov-Uvarov method. The bound state energy eigenvalues and the corresponding unnormalized eigenfunctions are obtained in terms of the Laguerre polynomials. The NU method is related to the solutions in terms of generalized Jacobi polynomials. In the NU method, the Schrödinger equation is reduced to a generalized equation of hypergeometric type using the coordinate transformation = (). The equation then yields a form whose polynomial solutions are given by the well-known Rodrigues relation. With the introduction of the IQYIQH potential into the Schrödinger equation, the resultant equation is further transformed in such a way that certain polynomials with four different possible forms are obtained. Out of these forms, only one form is suitable for use in obtaining the energy eigenvalues and the corresponding eigenfunctions of the Schrödinger equation.
Revista Mexicana de Física, 2022
In this paper, we investigate the new approximate bound state solution of deformed Klein--Gordon, Dirac and Schr\"{o}dinger equations in the symmetries of extended relativistic quantum mechanics ERQM and extended nonrelativistic quantum mechanics ENRQM have been obtained with a newly proposed potential called improved Hellmann-generalized Morse potential (IHGMP, for short). To the best of our knowledge, this problem is examined in literature in the usual RQM and NRQM with Hellmann-generalized Morse potential. The potential is a superposition of Hellmann potential, generalized Morse or Deng-Fan potential, and some other exponential terms. By employing the improved approximation to deal with the centrifugal term, Bopp's shift and standard perturbation theory method. The new approximate analytical energy shift and the corrections of bound state energyeigenvalues in ERQM and ENRQM are obtained for some selected diatomic molecules such as (HCl, LiH, H2, ScH, TiH, VH, CrH, CuLi, ...
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.
Revista Mexicana de Física
In this research work, within the framework of relativistic and nonrelativistic noncommutative quantum mechanics, the deformed Klein–Gordon and Schrödinger equations were solved with the modified equal vector scalar Manning-Rosen potential that has been of significance interest in recent years using Bopp's shift method and standard perturbation theory in the first-order in the noncommutativity parameters in 3-dimensions noncommutative quantum mechanics. By employing the improved approximation of the centrifugal term, the relativistic and nonrelativistic bound state energies were obtained for some diatomic molecules such as (HCl, CH, LiH, CO, NO, O2, I2, N2, H2, and Ar2). The obtained energy eigenvalues appear as a function of the generalized Gamma function, the parameters of noncommutativity, and the parameters of studied potential, in addition to the atomic quantum numbers . In both relativistic and nonrelativistic problems, we show that the corrections on the spectrum energy ...