On the evaluation of the norm of an integral operator associated with the stability of one-electron atoms

DOI10.1017/S030821050003002XzbMath0917.47057arXivmath/9801074MaRDI QIDQ4223666

Victor I. Burenkov, W. Desmond Evans

Publication date: 8 August 1999

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9801074

zbMATH Keywords

integral operatorwave decompositionnuclear chargerelativistic one-electron atoms

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of operator theory in the physical sciences (47N50) Integral operators (47G10)

Related Items

A variational approach to the Brown-Ravenhall operator for the relativistic one-electron atoms ⋮ THE RELATIVISTIC MEAN-FIELD EQUATIONS OF THE ATOMIC NUCLEUS ⋮ The spectrum of relativistic atoms according to Bethe and Salpeter and beyond ⋮ Variational methods in relativistic quantum mechanics ⋮ BLOCK-DIAGONALIZATION OF OPERATORS WITH GAPS, WITH APPLICATIONS TO DIRAC OPERATORS ⋮ BORN–OPPENHEIMER APPROXIMATION FOR THE BROWN–RAVENHALL EQUATION ⋮ General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators ⋮ Domains for Dirac-Coulomb min-max levels ⋮ On the eigenvalues of operators with gaps. Application to Dirac operators ⋮ On the spectral properties of the Brown-Ravenhall operator

Cites Work

• The spectrum of relativistic one-electron atoms according to Bethe and Salpeter
• Strict Positivity of a Relativistic Hamiltonian Due to Brown and Ravenhall
• On the interaction of two electrons