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
TypeCommunication / Conférence
Conference title4th International Conference on Industrial and Applied Mathematics (ICIAM 1999)
Book titleMathematical models and methods for ab initio quantum chemistry
Book authorDefranceschi, Mireille; Le Bris, Claude
Number of pages246
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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 / Keywordsminimization; eigenvalues; Dirac operators
Showing items related by title and author.
General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators. Dolbeault, Jean; Esteban, Maria J.; Séré, Eric (2006) Article accepté pour publication ou publié