A minimax principle for eigenvalues in spectral gaps: Dirac operators with Coulomb potentials.

Griesemer, Marcel; Lewis, Roger T.; Siedentop, Heinz

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

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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.

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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...

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Discrete spectrum and principal functions of non-selfadjoint differential operator

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In this article, we consider the operator $L$ defined by the differential expression $ℓ (y) = - y^{''} + q (x) y, - \infty < x < \infty$ in $L_{2} (- \infty, \infty)$ , where $q$ is a complex valued function. Discussing the spectrum, we prove that $L$ has a finite number of eigenvalues and spectral singularities, if the condition $sup_{- \infty < x < \infty} \{exp (ϵ \sqrt{| x |}) | q (x) |\} < \infty, ϵ > 0$ holds. Later we investigate the properties of the principal functions corresponding to the eigenvalues and the spectral singularities.