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Variational characterization for eigenvalues of Dirac operators

Dolbeault, Jean; Esteban, Maria J.; Séré, Eric (2000), Variational characterization for eigenvalues of Dirac operators, Calculus of Variations and Partial Differential Equations, 10, 4, p. 321-347. http://dx.doi.org/10.1007/s005260010321

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Type
Article accepté pour publication ou publié
Date
2000
Journal name
Calculus of Variations and Partial Differential Equations
Volume
10
Number
4
Publisher
Springer
Pages
321-347
Publication identifier
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Author(s)
Dolbeault, Jean cc
Esteban, Maria J. cc
Séré, Eric
Abstract (EN)
In this paper we give two different variational characterizations for the eigenvalues of H+V where H denotes the free Dirac operator and V is a scalar potential. The first one is a min-max involving a Rayleigh quotient. The second one consists in minimizing an appropriate nonlinear functional. Both methods can be applied to potentials which have singularities as strong as the Coulomb potential.
Subjects / Keywords
Dirac operators; relativistic quantum mechanics; eigenvalues; min-max; minimization; Rayleigh-Ritz technique