1999/09/14 by G. B. Deineka, G. B. Deĭneka, Deineka, G. B.
Engineering · Mathematics · Physics and Astronomy · #Astrophysics (astro-ph) #Basis (linear algebra) #Basis function #Dirac (video compression format) #Dirac equation #Electromagnetic Simulation and Numerical Methods #FOS: Physical sciences #Fock space #Geometry #Hermitian matrix #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Numerical methods in engineering #Physics #Quadrature (astronomy) #Quantum Mechanics and Non-Hermitian Physics #Quantum electrodynamics #Quantum mechanics #Wave function #astro-ph
paper · pdf · doi:10.48550/arxiv.astro-ph/9909229
10 pages
arxiv created 1999/09/14 · openalex publication_date 1999/09/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A two-dimensional, fully numerical approach to the solution of four-component Dirac-Fock equation using the moderately long Hermitian basis of B-splines is applied to H, H2+ and H2 in a strong magnetic field. The geometric parameters, including different behavior of wave-functions relativistic components are analyzed. The accuracy of the solutions as a function of the basis lenght is estimated. The relativistic corrections are calculated by transformation of the matrix equations to the equations for large relativistic components. Application of the finite-element method to solution of the Dirac-Fock equation without supplementary assumption about exchange in case of the H2 excited states is discussed. The maximum localization of the basis functions provides applicability of the quadrature formulae for five-dimensional two-electron integral calculations within reasonable period.