Variational characterization for eigenvalues of Dirac operators

By Jean Dolbeault, Maria J. Esteban, É. Séré. 2000

62 citations recorded by the source corpus.

Abstract. 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.

Subfields: Applied Mathematics, Mathematical Physics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/3976cdf141c1532bca4bfecb9cf102129cee1ec6

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In Applied Mathematics

In Mathematical Physics

In Mechanics of Materials

Citations in the corpus

Variational methods in relativistic quantum mechanics (2007, background): “This was mentioned in several papers dealing with numerical computations of Dirac eigenvalues before it was formally addressed in different contexts in a series of papers [63, 81, 80, 50, 51].”
From atoms to crystals: a mathematical journey (2005, background): “[85, 86] Minimax characterization of the eigenvalues of the atomic Dirac Hamiltonian Assume Z < c.”