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6 papers · 1 filter
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…
Structural Algebraic Quantum Field Theory
A. D. Alhaidari
Conventional quantum field theory is a method for studying structureless elementary particles. Non-elementary particles, on the other hand, are those with internal structure or par…
J-matrix method of scattering for inverse-square singular potentials with supercritical coupling II. Regularization
Abdulaziz D. Alhaidari, Hocine Bahlouli, S. M. Al-Marzoug +1
This paper is a continuation of the previous one [Journal xx, xxxxx (2022)]. Here, we reformulate the same J-matrix theory by regularizing the inverse square singular potential. Th…
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…