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
TypeArticle accepté pour publication ou publié
Journal nameCalculus of Variations and Partial Differential Equations
MetadataShow full item record
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 / KeywordsDirac operators; relativistic quantum mechanics; eigenvalues; min-max; minimization; Rayleigh-Ritz technique
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