M. Essaouini | Searcharxiv

arXiv2019

One-Center Nonrelativistic Integrals of Second Order for the NMR Shielding Tensor

This work presents the analytical development of one-center nonrelativistic integrals of second order for the NMR (nuclear magnetic resonance) shielding tensor. The main difficulty in the analytical and numerical treatments of these integrals arise from the presence of $r^{-3}$ in the operator. Compact analytical formulae are obtained using the Fourier transform formalism. Moreover, the obtained formulae are computationally convenient and can be computed to machine accuracy.

physics.comp-ph↗

arXiv2018

Computation of Energy Eigenvalues of the Anharmonic Coulombic Potential with Irregular Singularities

The present contribution concerns the computation of energy eigenvalues of a perturbed anharmonic coulombic potential with irregular singularities using a combination of the Sinc collocation method and the double exponential transformation. This method provides a highly efficient and accurate algorithm to compute the energy eigenvalues of one-dimensional time-independent Schr\"odinger equation. The numerical results obtained illustrate clearly the highly efficiency and accuracy of the proposed method. All our codes are written in Julia and are available on github at \url{https://github.com/pjgaudre/DESincEig.jl}.

math.NA↗