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Variational methods in relativistic quantum mechanics: new approach to the computation of Dirac eigenvalues

  • Jean Dolbeault
  • Maria J. Esteban
  • Eric Séré
Part of the Lecture Notes in Chemistry book series (LNC, volume 74)

Abstract

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 offunctions 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.

Keywords

Dirac Operator Rayleigh Quotient Relativistic Quantum Mechanic Finite Basis Minimax Principle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Jean Dolbeault
    • 1
  • Maria J. Esteban
    • 1
  • Eric Séré
    • 1
  1. 1.CEREMADE (UMR CNRS 7534)Université Paris-DauphineParis Cedex 16France

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