10 citations · 18 across the 8 of their papers we have counts for
9 papers
Zernike polynomials from the tridiagonalization of the radial harmonic oscillator in displaced Fock states
Hashim A. Yamani, Zouhaïr Mouayn
We revisit the J-matrix method for the one dimensional radial harmonic oscillator (RHO) and construct its tridiagonal matrix representation within an orthonormal basis phi(z)n of L…
Generalized coherent states for the harmonic oscillator by the J-matrix method with an extension to the Morse potential
Hashim A. Yamani, Zouhaïr Mouayn
While dealing with the J-Matrix method for the harmonic oscillator to write down its tridiagonal matrix representation in an orthonormal basis of L2(R); we rederive a set of genera…
Coherent states associated with tridiagonal Hamiltonians
Hashim A. Yamani, Zouhaïr Mouayn
It has been shown that a positive semi-definite Hamiltonian H, that has a tridiagonal matrix representation in a given basis, can be represented in the form H = A†A, where A is a f…
Coherent States of Systems with Pure Continuous Energy Spectra
Zouhair Mouayn, Hashim A. Yamani
While dealing with a Hamiltonian with continuous spectrum we use a tridiagonal method involving orthogonal polynomials to construct a set of coherent states obeying a Glauber-type…
Iterative polynomial-root-finding procedure with enhanced accuracy
Hashim A. Yamani, Abdulaziz D. Alhaidari
We devise a simple but remarkably accurate iterative routine for calculating the roots of a polynomial of any degree. We demonstrate that our results have significant improvement i…
Properties of shape-invariant tridiagonal Hamiltonians
Hashim A. Yamani, Zouhaïr Mouayn
It has been established that a positive semi-definite Hamiltonian,, that has a tridiagonal matrix representation in a basis set, allows a definition of forward (and backward) sh…
Supersymmetry of the Morse oscillator
Hashim A Yamani, Zouhair Mouayn
While dealing in [1] with the supersymmetry of a tridiagonal Hamiltonian H, we have proved that its partner Hamiltonian H(+) also have a tridiagonal matrix representation in the sa…
Extension and exact realization of the Heller's derivative rule
Hashim A. Yamani, Abdulaziz D. Alhaidari
The accuracy of the Heller's derivative rule to calculate the numerical weights associated with discretized energy spectrum is enhanced by Broad's extension which adds (N-1) more i…
J-matrix method of scattering in any L2 basis
H. A. Yamani, A. D. Alhaidari, M. S. Abdelmonem
The restriction imposed on the J-matrix method of using specific L2 bases is lifted without compromising any of the advantages that it offers. This opens the door to a wider range…