Displaying similar documents to “A minimax principle for eigenvalues in spectral gaps: Dirac operators with Coulomb potentials.”

Algebraic spectral gaps

Amaury Mouchet (2012)

ESAIM: Proceedings

Similarity:

For the one-dimensional Schrödinger equation, some real intervals with no eigenvalues (the spectral gaps) may be obtained rather systematically with a method proposed by H. Giacomini and A. Mouchet in 2007. The present article provides some alternative formulation of this method, suggests some possible generalizations and extensively discusses the higher-dimensional case.

General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators

Jean Dolbeault, Maria Esteban, Eric Séré (2006)

Journal of the European Mathematical Society

Similarity:

This paper is concerned with an extension and reinterpretation of previous results on the variational characterization of eigenvalues in gaps of the essential spectrum of self-adjoint operators. We state two general abstract results on the existence of eigenvalues in the gap and a continuation principle. Then these results are applied to Dirac operators in order to characterize simultaneously eigenvalues corresponding to electronic and positronic bound states.

On the characterization of scalar type spectral operators

P. A. Cojuhari, A. M. Gomilko (2008)

Studia Mathematica

Similarity:

The paper is concerned with conditions guaranteeing that a bounded operator in a reflexive Banach space is a scalar type spectral operator. The cases where the spectrum of the operator lies on the real axis and on the unit circle are studied separately.

Dynamical Resonances and SSF Singularities for a Magnetic Schrödinger Operator

Astaburuaga, María Angélica, Briet, Philippe, Bruneau, Vincent, Fernández, Claudio, Raikov, Georgi (2008)

Serdica Mathematical Journal

Similarity:

We consider the Hamiltonian H of a 3D spinless non-relativistic quantum particle subject to parallel constant magnetic and non-constant electric field. The operator H has infinitely many eigenvalues of infinite multiplicity embedded in its continuous spectrum. We perturb H by appropriate scalar potentials V and investigate the transformation of these embedded eigenvalues into resonances. First, we assume that the electric potentials are dilation-analytic with respect to the variable...