Accurate solution of the Dirac equation on Lagrange meshes

Accurate solution of the Dirac equation on Lagrange meshes.

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 ...

Interconnection of Dirac Structures and Lagrange-Dirac Dynamical Systems

In the paper, we develop an idea of interconnection of Dirac structures and their associated LagrangeDirac dynamical systems. First, we briefly review the LagrangeDirac dynamical systems (namely, implicit Lagrangian systems) associated to induced Dirac structures. Second, we describe an idea of interconnection of Dirac structures; namely, we show how two distinct Lagrange-Dirac systems can be i...

Semi-analytical Solution of Dirac equation in Schwarzschild Geometry

A Z-dependent variational solution of Thomas-Fermi-Dirac equation

Using Thomas-Fermi-Dirac equation within the exchange-correlation scheme and a Z-dependent trial solution, the ground state binding energy for neutral, positively, and negatively charged atoms are calculated. Comparing to the results obtained in earlier works, the values of the binding energy estimated here for both light and heavy atoms agree nicely with the Hartree-Fock values. We have also c...

Three-dimensional Finite Difference-Time Domain Solution of Dirac Equation

The Dirac equation is solved using three-dimensional Finite DifferenceTime Domain (FDTD) method. Zitterbewegung and the dynamics of a well-localized electron are used as examples of FDTD application to the case of free electrons. PACS numbers: 03.65.Pm, 02.60.-x, 02.60.Lj § Correspondence should be addressed to Louisiana Tech University, PO Box 10348, Ruston, LA 71272, Tel: +1.318.257.3591, Fax...