Minimax principles, Hardy-Dirac inequalities, and operator cores for two and three dimensional Coulomb-Dirac operators

zbMath1350.49074arXiv1603.01557MaRDI QIDQ321898

David Müller

Publication date: 14 October 2016

Published in: Documenta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.01557

zbMATH Keywords

eigenvaluesminimax principleCoulomb-Dirac operatorHardy-Dirac inequality

Mathematics Subject Classification ID

Existence of solutions for minimax problems (49J35) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Variational methods for eigenvalues of operators (49R05)

Related Items

On the virtual levels of positively projected massless Coulomb-Dirac operators, Which Nuclear Shape Generates the Strongest Attraction on a Relativistic Electron? An Open Problem in Relativistic Quantum Mechanics, Distinguished self-adjoint extension and eigenvalues of operators with gaps. Application to Dirac-Coulomb operators, Lower bounds on the moduli of three-dimensional Coulomb-Dirac operators via fractional Laplacians with applications, Strichartz estimates for the 2D and 3D massless Dirac-Coulomb equations and applications, The Scott conjecture for large Coulomb systems: a review, Accumulation rate of bound states of dipoles generated by point charges in strained graphene, Boundary triples for the Dirac operator with Coulomb-type spherically symmetric perturbations, Friedrichs extension and min-max principle for operators with a gap, Critical magnetic field for 2D magnetic Dirac-Coulomb operators and Hardy inequalities, Domains for Dirac-Coulomb min-max levels, Dirac-Coulomb operators with general charge distribution. I: Distinguished extension and min-max formulas, Corrigendum to: ``On the eigenvalues of operators with gaps. Application to Dirac operators