Affiliation:
1. Department of Mathematics, Imperial College London, London SW7 2AZ, UK
Abstract
We present new results on the block-diagonalization of operators with spectral gaps, based on a method of Langer and Tretter, and apply them to Dirac operators on three-dimensional Euclidean space with unbounded potentials. For the Coulomb potential, we achieve an exact diagonalization up to nuclear charge Z = 124 (which covers all chemical elements) and prove the convergence of an approximate block-diagonalization up to Z = 62, thus considerably improving the upper bounds Z = 93 and Z = 51, respectively, established by Siedentop and Stockmeyer.
Publisher
World Scientific Pub Co Pte Lt
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Topological obstructions to the diagonalisation of pseudodifferential systems;Proceedings of the American Mathematical Society, Series B;2022-12-27
2. Diagonalization of elliptic systems via pseudodifferential projections;Journal of Differential Equations;2022-03
3. The Tan $2 \Theta$ Theorem in fluid dynamics;Journal of Spectral Theory;2019-09-12
4. Non-symmetric perturbations of self-adjoint operators;Journal of Mathematical Analysis and Applications;2016-09
5. On Invariant Graph Subspaces;Integral Equations and Operator Theory;2016-05-05