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- King Fahd University of Petroleum and MineralsSA54 papers
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41 papers · 1 filter
Matrix representation of the resolvent operator in square-integrable basis and physical application
A. D. Alhaidari
We obtain simple formulas for the matrix elements of the resolvent operator (the Green's function) in any finite set of square integrable basis. These formulas are suitable for num…
Energy spectrum design and potential function engineering
A. D. Alhaidari, T. J. Taiwo
Starting with an orthogonal polynomial sequence that has a discrete spectrum, we design an energy spectrum formula, , where $|{s_k\}$ is th…
Electrostatic multipole contributions to the binding energy of electrons
A. D. Alhaidari, H. Bahlouli
The interaction of an electron with a local static charge distribution (e.g., an atom or molecule) is dominated at large distances by the radial 1/r Coulomb potential. The second o…
Solutions of the scattering problem in a complete set of Bessel functions with a discrete index
A. D. Alhaidari, M. E. H. Ismail
We use the tridiagonal representation approach to solve the radial Schrödinger equation for the continuum scattering states of the Kratzer potential. We do the same for a radial po…
Progressive approximation of bound states by finite series of square-integrable functions
A. D. Alhaidari
We use the "tridiagonal representation approach" to solve the time-independent Schrödinger equation for bound states in a basis set of finite size. We obtain two classes of solutio…
Bound-states for generalized trigonometric and hyperbolic Pöschl-Teller potentials
A. D. Alhaidari, I. A. Assi, A. Mebirouk
We use the "tridiagonal representation approach" to solve the time-independent Schrödinger equation for the bound states of generalized versions of the trigonometric and hyperbolic…