Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis

Journal Article · Mon Feb 15 00:00:00 EST 2016 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2015.11.024· OSTI ID:22570223

Fillion-Gourdeau, F., E-mail: [e-mail] ^[1]; Centre de Recherches Mathématiques, Université de Montréal, Montréal, H3T 1J4 ^[2]; Lorin, E., E-mail: [e-mail] ^[3]; Centre de Recherches Mathématiques, Université de Montréal, Montréal, H3T 1J4 ^[2]; Bandrauk, A.D., E-mail: [e-mail] ^[4]; Centre de Recherches Mathématiques, Université de Montréal, Montréal, H3T 1J4 ^[2]

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1. Université du Québec, INRS – Énergie, Matériaux et Télécommunications, Varennes, J3X 1S2 (Canada)
2. (Canada)
3. School of Mathematics and Statistics, Carleton University, Ottawa, K1S 5B6 (Canada)
4. Laboratoire de Chimie Théorique, Faculté des Sciences, Université de Sherbrooke, Sherbrooke, J1K 2R1 (Canada)

A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron–molecular two-center system. The initial state is evaluated from a variational principle using a kinetic/atomic balanced basis, which allows for an efficient and accurate determination of the Dirac spectrum and eigenfunctions. B-spline basis functions are used to obtain high accuracy. This numerical method is used to compute the energy spectrum of the two-center problem and then the evolution of eigenstate wavefunctions in an external electromagnetic field.

• OSTI ID: 22570223
• Journal Information: Journal of Computational Physics, Vol. 307; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCURACY
COORDINATES
DIRAC EQUATION
EIGENFUNCTIONS
EIGENSTATES
ELECTROMAGNETIC FIELDS
ENERGY SPECTRA
TIME DEPENDENCE
VARIATIONAL METHODS
WAVE FUNCTIONS