A variational approach to the Brown–Ravenhall operator for the relativistic one-electron atoms. (May 2016)

• Record Type: Journal Article
• Authors: Coti Zelati, Vittorio; Nolasco, Margherita
• Is Part Of: Nonlinear analysis. Volume 136(2016)
• Page Start: 62
• Page End: 83
• Publication Date: 2016-05
• Subjects: Brown–Ravenhall operator -- Dirac operator -- Variational methods; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.02.011
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the Brown–Ravenhall operator (the projection of the Dirac operator perturbed by a potential V ∈ L w 3 ) using the Foldy–Wouthuysen (unitary) transformation and its realization as an elliptic problem in the 4-dim half space R + 4 with Neumann boundary condition. Using this approach we give a characterization of its eigenvalues and eigenfunctions alternative to the classical Rayleigh quotients.