Abstract
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 singularity. For hydrogenic atoms, numerically exact energies and wave functions are obtained with small numbers of mesh points, where is the principal quantum number. Numerically exact mean values of powers to 3 of the radial coordinate can also be obtained with mesh points. For the Yukawa potential, a 15-digit agreement with benchmark energies of the literature is obtained with 50 or fewer mesh points.
- Received 12 February 2014
DOI:https://doi.org/10.1103/PhysRevE.89.043305
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