arXiv subjects
Publications and source records attributed to Maen Odeh.
The pseudoperturbative shifted - $l$ expansion technique PSLET is employed to study the spectra of 2D H-donors in magnetic field. The Zeeman effect is investigated and results are found to be excellent compared to those in ref.[14].
Magnetic fingerprints on the spectra of an interacting electron with a negatively charged ion in a parabolic quantum dot (QD), and of two interacting electrons in such a dot, are investigated via a pseudoperturbative methodical proposal. The effect of ion-electron and electron-electron interactions on the spectra are studied. The effect of the symmetry of such problem is emphasized. Compared to those obtained by Zhu et al. [6], via a series solution, the results are found in excellent accord. Higher excited - states are also reported.
We propose a new analytical method to solve for nonexactly soluble Schrodinger equation via expansions through some existing quantum numbers. Successfully, it is applied to the rational non-polynomial oscillator potential. Moreover, a conclusion reached by Scherrer et al. [2], via matrix continued fractions method, that the shifted large N expansion method leads to dubious accuracies is investigated. The cutoff - Coulomb and Coulomb plus logarithmic potentials are also investigated.
The pseudoperturbative shifted - $l$ expansion technique PSLET [12,16] is generalized for states with arbitrary number of nodal zeros. Interdimensional degeneracies, emerging from the isomorphism between angular momentum and dimensionality of the central force Schrödinger equation, are used to construct part of the D - dimensional anharmonic oscillator bound - state spectra. PSLET results are found to compare excellently with those from a series [5], exact and open perturbation [9] solutions.
The pseudoperturbative shifted - $l$ expansion technique PSLET is generalized for states with arbitrary number of nodal zeros. Bound- states energy eigenvalues for two truncated coulombic potentials are calculated using PSLET. In contrast with shifted large-N expansion technique, PSLET results compare excellently with those from direct numerical integration.
The energy levels of neutral atoms supported by Yukawa potential, $V(r)=-Z exp(-αr)/r$, are studied, using both dimensional and dimensionless quantities, via a new analytical methodical proposal (devised to solve for nonexactly solvable Schrodinger equation). Using dimensionless quantities, by scaling the radial Hamiltonian through $y=Zr$ and $α^{'}=α/Z$, we report that the scaled screening parameter $α^{'}$ is restricted to have values ranging from zero to less than 0.4. On the other hand, working with the scaled Hamiltonian enhances the accuracy and extremely speeds up the convergence of the energy eigenvalues. The energy levels of several new eligible scaled screening parameter $α^{'}$ values are also reported.
The pseudoperturbative shifted - l expansion technique PSLET [5,20] is generalized for states with arbitrary number of nodal zeros. Interdimensional degeneracies, emerging from the isomorphism between angular momentum and dimensionality of the central force Schrodinger equation, are used to construct part of the D - dimensional spiked harmonic oscillator bound - states. PSLET results are found to compare excellenly with those from direct numerical integration and generalized variational methods [1,2].
A new pseudoperturbative (artificial in nature) methodical proposal [15] is used to solve for Schrodinger equation with a class of phenomenologically useful and methodically challenging anharmonice oscillator potentials V(q)=α_o q^2 + αq^4. The effect of the [4,5] Pade' approximant on the leading eigenenergy term is studied. Comparison with results from numerical (exact) and several eligible (approximation) methods is made.
The pseudoperturbative shifted-l expansion technique (PSLET) is introduced to determine nodeless states of the 2D Schrodinger equation with an arbitrary cylindrically symmetric potentials. Exact energy eigenvalues and eigenfunctions for the 2D Coulomb and harmonic oscillator potentials are reproduced. Moreover, exact energy eigenvalues, compared to those obtained by numerical solution [11], were obtained for the hybrid of the 2D Coulomb and oscillator potentials.
A shifted - l expansion technique is introduced to calculate the energy eigenvalues for Klein-Gordon (KG) equation with Lorentz vector and/or Lorentz scalar potentials. Although it applies to any spherically symmetric potential, those that include Coulomb-like terms are only considered. Exact eigenvalues for a Lorentz vector or a Lorentz scalar, and an equally mixed Lorentz vector and Lorenz scalar Coulombic potentials are reproduced. Highly accurate and rapidly converging ground-state energies for Lorentz vector Coulomb with a Lorentz scalar linear potential, V(r)=-A1/r+kr, and S(r)=kr, respectively, are obtained. Moreover, a simple straightforward closed-form solution for a KG-particle in a Coulombic Lorentz vector and Lorentz scalar potentials is presented in appendix A.
We propose a new analytical method to solve for the nonexactly solvable Schrodinger equation. Successfully, it is applied to a class of spiked harmonic oscillators and truncated Coulomb potentials. The utility of this method could be extended to study other systems of atomic, molecular and nuclear physics interest.
The quasi-relativistic harmonic oscillator bound states constructed by Znojil (J. Phys. A: Math. Gen. 29 (1999)2905) are investigated via a new methodical proposal. Compared with those obtained by an anonymous referee (from a direct numerical integration method)of Znojil's paper, our results appear to be more favourable than those obtained by Znojil via quasi-perturbation, variational, Hill-determinant and Riccati-Pade' methods. Bound states with larger angular momenta l, are also constructed.