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Variational Methods in Relativistic Quantum Mechanics: New Approach to the Computation of Dirac Eigenvalues

Dolbeault, Jean; Esteban, Maria J.; Séré, Eric (2000), Variational Methods in Relativistic Quantum Mechanics: New Approach to the Computation of Dirac Eigenvalues, in Defranceschi, Mireille; Le Bris, Claude, Mathematical models and methods for ab initio quantum chemistry, Springer : Berlin, p. 211-226

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Type
Communication / Conférence
Date
2000
Conference title
4th International Conference on Industrial and Applied Mathematics (ICIAM 1999)
Conference date
1999-07
Conference city
Edimbourg
Conference country
Royaume-Uni
Book title
Mathematical models and methods for ab initio quantum chemistry
Book author
Defranceschi, Mireille; Le Bris, Claude
Publisher
Springer
Published in
Berlin
ISBN
3-540-67631
Number of pages
246
Pages
211-226
Metadata
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Author(s)
Dolbeault, Jean cc
Esteban, Maria J. cc
Séré, Eric
Abstract (EN)
The main goal of this paper is to describe some new variational methods for the characterization and computation of the eigenvalues and the eigenstates of Dirac operators. Our methods are all based on exact variational principles, both of min-max and of minimization types. The minimization procedure that we introduce is done in a particular set of functions satisfying a nonlinear constraint. Finally, we present several numerical methods that we have implemented in particular cases, in order to construct approximate solutions of that minimization problem.
Subjects / Keywords
minimization; eigenvalues; Dirac operators