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

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Date
2000
Dewey
Analyse
Sujet
minimization; eigenvalues; Dirac operators
Conference name
4th International Conference on Industrial and Applied Mathematics (ICIAM 1999)
Conference date
07-1999
Conference city
Edimbourg
Conference country
Royaume-Uni
Book title
Mathematical models and methods for ab initio quantum chemistry
Author
Defranceschi, Mireille; Le Bris, Claude
Publisher
Springer
Publisher city
Berlin
Year
2000
Pages number
246
ISBN
3-540-67631
URI
https://basepub.dauphine.fr/handle/123456789/6702
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  • CEREMADE : Publications
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Author
Dolbeault, Jean
Esteban, Maria J.
Séré, Eric
Type
Communication / Conférence
Item number of pages
211-226
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.

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