par Baye, Daniel Jean 
;Filippin, Livio ;Godefroid, Michel
Référence Physical review. E, Statistical, nonlinear, and soft matter physics, 89, page (1-9), 043305
Publication Publié, 2014-04-10
;Filippin, Livio ;Godefroid, Michel Référence Physical review. E, Statistical, nonlinear, and soft matter physics, 89, page (1-9), 043305
Publication Publié, 2014-04-10
Article révisé par les pairs
| Résumé : | The Lagrange-mesh method is an approximate variational method taking the form of equations on a grid because of the use of a Gauss quadrature approximation. With a basis of Lagrange functions involving associated Laguerre polynomials related to the Gauss quadrature, the method is applied to the Dirac equation. The potential may possess a 1/r singularity. For hydrogenic atoms, numerically exact energies and wave functions are obtained with small numbers n + 1 of mesh points, where n is the principal quantum number. Numerically exact mean values of powers −2 to 3 of the radial coordinate r can also be obtained with n + 2 mesh points. For the Yukawa potential, a 15-digit agreement with benchmark energies of the literature is obtained with 50 or fewer mesh points. |
