Omar Mustafa - Academia.edu (original) (raw)

Papers by Omar Mustafa

Research paper thumbnail of Ja n 20 01 A pseudo-perturbative expansions method ; nonpolynomial , cutoff-Coulomb , and Coulomb plus logarithmic potentials

We propose a new analytical method to solve for nonexactly soluble Schrödinger equation via expan... more We propose a new analytical method to solve for nonexactly soluble Schrödinger equation via expansions through some existing quantum numbers. Successfully, it is applied to the rational nonpolynomial 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.

Research paper thumbnail of v 1 1 N ov 1 99 9 2 D H-atom in an arbitrary magnetic field via pseudoperturbation expansions through the quantum number l

The pseudoperturbative shifted l expansion technique (PSLET) is introduced to determine nodeless ... more The pseudoperturbative shifted l expansion technique (PSLET) is introduced to determine nodeless states of the 2D Schrödinger equation with arbitrary cylindrically symmetric potentials. Exact energy eigenvalues and eigenfunctions for the 2D Coulomb and harmonic oscillator potentials are reproduce. Moreover, exact energy eigenvalues, compared to those obtained by numerical solution [11], were obtained for the hybrid of the 2D Coulomb and oscillator potentials.

Research paper thumbnail of Magnetic Fingerprints on the Spectra of One Electron and Two Electrons Interacting in Parabolic Quantum Dots

Magnetic fingerprints on the spectra of an electron interacting with a negatively charged ion in ... more Magnetic fingerprints on the spectra of an electron interacting with a negatively charged ion in a parabolic quantum dot (QD), and of two interacting electrons in such a dot, are investigated via a new pseudoperturbative methodical proposal. The effects of ion-electron and electron-electron interactions on the spectra are studied. The effect of the symmetry of such problem is emphasized. Compared with those obtained by Zhu et al.[6], via a series solution, the results are found in excellent accord. Higher excited-states are also reported.

Research paper thumbnail of Energy Levels of Neutral Atoms Via a New Perturbation Method

The energy levels of neutral atoms supported by Yukawa potential, V (r) = −Zexp(−αr)/r, are studi... more The energy levels of neutral atoms supported by Yukawa potential, V (r) = −Zexp(−αr)/r, are studied, using both dimensional and dimensionless quantities, via a new analytical methodical proposal (devised to solve for nonexactly solvable Schrödinger 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.

Research paper thumbnail of 2D H-Atom in an Arbitrary Magnetic Field via Pseudoperturbation Expansions Through the Quantum Number l

Communications in Theoretical Physics, 2000

The pseudoperturbative shiftedl expansion technique (PSLET) is introduced to determine nodeless s... more The pseudoperturbative shiftedl expansion technique (PSLET) is introduced to determine nodeless states of the 2D Schrödinger equation with arbitrary cylindrically symmetric potentials. Exact energy eigenvalues and eigenfunctions for the 2D Coulomb and harmonic oscillator potentials are reproduce. Moreover, exact energy eigenvalues, compared to those obtained by numerical solution [11], were obtained for the hybrid of the 2D Coulomb and oscillator potentials.

Research paper thumbnail of Bound states for spiked harmonic oscillators and truncated Coulomb potentials

Journal of Physics B: Atomic, Molecular and Optical Physics, 1999

We propose a new analytical method to solve for the nonexactly solvable Schrödinger equation. Suc... more We propose a new analytical method to solve for the nonexactly solvable Schrödinger 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.

Research paper thumbnail of Quasi-relativistic harmonic oscillator bound states

Journal of Physics A: Mathematical and General, 1999

The quasi-relativistic harmonic oscillator bound-states constructed by Znojil (1996 J. Phys. A29 ... more The quasi-relativistic harmonic oscillator bound-states constructed by Znojil (1996 J. Phys. A29 2905) are investigated via a new methodical proposal. Compared to those obtained by an anonymous referee (from a direct numerical integration method) of Znojil's paper [3], our results appeared to be more favorable than those obtained by Znojil via quasi-perturbative, variational, Hill-determinant and Riccati-Padé methods. Bound-states with larger angular momenta l are also constructed.

Research paper thumbnail of Part of the D -dimensional spiked harmonic oscillator spectra

Journal of Physics A: Mathematical and General, 2000

The pseudoperturbative shiftedl expansion technique PSLET [5,20] is generalized for states with a... more The pseudoperturbative shiftedl 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 Schrödinger equation, are used to construct part of the D-dimensional spiked harmonic oscillator bound-state spectra. PSLET results are found to compare excellently with those from direct numerical integration and generalized variational methods [1,2].

Research paper thumbnail of Bound states for truncated Coulomb potentials

Journal of Physics A: Mathematical and General, 2000

The pseudoperturbative shiftedl expansion technique PSLET [16-19] is generalized for states with ... more The pseudoperturbative shiftedl expansion technique PSLET [16-19] 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.

Research paper thumbnail of Anharmonic oscillators energies via artificial perturbation method

The European Physical Journal B, 2000

A new pseudoperturbative (artificial in nature) methodical proposal [15] is used to solve for Sch... more A new pseudoperturbative (artificial in nature) methodical proposal [15] is used to solve for Schrödinger equation with a class of phenomenologically useful and methodically challenging anharmonic oscillator potentials V (q) = α o q 2 + αq 4. The effect of the [4,5] Padé approximant on the leading eigenenergy term is studied. Comparison with results from numerical (exact) and several eligible (approximation) methods is made.

Research paper thumbnail of Ja n 20 01 A pseudo-perturbative expansions method ; nonpolynomial , cutoff-Coulomb , and Coulomb plus logarithmic potentials

We propose a new analytical method to solve for nonexactly soluble Schrödinger equation via expan... more We propose a new analytical method to solve for nonexactly soluble Schrödinger equation via expansions through some existing quantum numbers. Successfully, it is applied to the rational nonpolynomial 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.

Research paper thumbnail of v 1 1 N ov 1 99 9 2 D H-atom in an arbitrary magnetic field via pseudoperturbation expansions through the quantum number l

The pseudoperturbative shifted l expansion technique (PSLET) is introduced to determine nodeless ... more The pseudoperturbative shifted l expansion technique (PSLET) is introduced to determine nodeless states of the 2D Schrödinger equation with arbitrary cylindrically symmetric potentials. Exact energy eigenvalues and eigenfunctions for the 2D Coulomb and harmonic oscillator potentials are reproduce. Moreover, exact energy eigenvalues, compared to those obtained by numerical solution [11], were obtained for the hybrid of the 2D Coulomb and oscillator potentials.

Research paper thumbnail of Magnetic Fingerprints on the Spectra of One Electron and Two Electrons Interacting in Parabolic Quantum Dots

Magnetic fingerprints on the spectra of an electron interacting with a negatively charged ion in ... more Magnetic fingerprints on the spectra of an electron interacting with a negatively charged ion in a parabolic quantum dot (QD), and of two interacting electrons in such a dot, are investigated via a new pseudoperturbative methodical proposal. The effects of ion-electron and electron-electron interactions on the spectra are studied. The effect of the symmetry of such problem is emphasized. Compared with those obtained by Zhu et al.[6], via a series solution, the results are found in excellent accord. Higher excited-states are also reported.

Research paper thumbnail of Energy Levels of Neutral Atoms Via a New Perturbation Method

The energy levels of neutral atoms supported by Yukawa potential, V (r) = −Zexp(−αr)/r, are studi... more The energy levels of neutral atoms supported by Yukawa potential, V (r) = −Zexp(−αr)/r, are studied, using both dimensional and dimensionless quantities, via a new analytical methodical proposal (devised to solve for nonexactly solvable Schrödinger 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.

Research paper thumbnail of 2D H-Atom in an Arbitrary Magnetic Field via Pseudoperturbation Expansions Through the Quantum Number l

Communications in Theoretical Physics, 2000

The pseudoperturbative shiftedl expansion technique (PSLET) is introduced to determine nodeless s... more The pseudoperturbative shiftedl expansion technique (PSLET) is introduced to determine nodeless states of the 2D Schrödinger equation with arbitrary cylindrically symmetric potentials. Exact energy eigenvalues and eigenfunctions for the 2D Coulomb and harmonic oscillator potentials are reproduce. Moreover, exact energy eigenvalues, compared to those obtained by numerical solution [11], were obtained for the hybrid of the 2D Coulomb and oscillator potentials.

Research paper thumbnail of Bound states for spiked harmonic oscillators and truncated Coulomb potentials

Journal of Physics B: Atomic, Molecular and Optical Physics, 1999

We propose a new analytical method to solve for the nonexactly solvable Schrödinger equation. Suc... more We propose a new analytical method to solve for the nonexactly solvable Schrödinger 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.

Research paper thumbnail of Quasi-relativistic harmonic oscillator bound states

Journal of Physics A: Mathematical and General, 1999

The quasi-relativistic harmonic oscillator bound-states constructed by Znojil (1996 J. Phys. A29 ... more The quasi-relativistic harmonic oscillator bound-states constructed by Znojil (1996 J. Phys. A29 2905) are investigated via a new methodical proposal. Compared to those obtained by an anonymous referee (from a direct numerical integration method) of Znojil's paper [3], our results appeared to be more favorable than those obtained by Znojil via quasi-perturbative, variational, Hill-determinant and Riccati-Padé methods. Bound-states with larger angular momenta l are also constructed.

Research paper thumbnail of Part of the D -dimensional spiked harmonic oscillator spectra

Journal of Physics A: Mathematical and General, 2000

The pseudoperturbative shiftedl expansion technique PSLET [5,20] is generalized for states with a... more The pseudoperturbative shiftedl 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 Schrödinger equation, are used to construct part of the D-dimensional spiked harmonic oscillator bound-state spectra. PSLET results are found to compare excellently with those from direct numerical integration and generalized variational methods [1,2].

Research paper thumbnail of Bound states for truncated Coulomb potentials

Journal of Physics A: Mathematical and General, 2000

The pseudoperturbative shiftedl expansion technique PSLET [16-19] is generalized for states with ... more The pseudoperturbative shiftedl expansion technique PSLET [16-19] 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.

Research paper thumbnail of Anharmonic oscillators energies via artificial perturbation method

The European Physical Journal B, 2000

A new pseudoperturbative (artificial in nature) methodical proposal [15] is used to solve for Sch... more A new pseudoperturbative (artificial in nature) methodical proposal [15] is used to solve for Schrödinger equation with a class of phenomenologically useful and methodically challenging anharmonic oscillator potentials V (q) = α o q 2 + αq 4. The effect of the [4,5] Padé approximant on the leading eigenenergy term is studied. Comparison with results from numerical (exact) and several eligible (approximation) methods is made.