A minimax principle for the eigenvalues in spectral gaps

Journal of the London Mathematical Society

Volumn 60, Issue 2, 1999, Pages 490-500

  Griesemer, Marcel ^a   Siedentop, Heinz ^a  

^a UNIVERSITY OF REGENSBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000060563     PISSN: 00246107     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024610799007930     Document Type: Article

References (20)

1. G. E. BROWN and D. G. RAVENHALL, 'On the interaction of two electrons', Proc. Roy. Soc. London Ser. A 208 (A 1095) (1951) 552-559.
2. R. COURANT and D. HILBERT, Methoden der Mathematischen Physik I, 3rd edn, Heidelberger Taschenbücher 30 (Springer, Berlin, 1968).
3. S. N. DATTA and G. DEVIAH, 'The minimax technique in relativistic Hartree-Fock calculations', Pramana 30 (1988) 387-405.
4. J. DOLBEAULT, M. J. ESTEBAN and E. SéRé, International Conference on Differential Equations and Mathematical Physics, Atlanta, Georgia, 23-29 March 1997.
5. G. W. F. DRAKE and S. P. GOLDMAN, ' Relativistic Sturmian and finite basis set methods in atomic physics', Adv. Atomic Molecular Phys. 25 (1988) 393-416.
6. W. D. EVANS, P. PERRY and H. SIEDENTOP, 'The spectrum of relativistic one-electron atoms according to Bethe and Salpeter', Comm, Math. Phys. 178 (1996) 733-746.
7. Y. ISHIKAWA and K. Koc, 'Relativistic many-body perturbation theory based on the no-pair Dirac-Coulomb-Breit Hamiltonian : relativistic correlation energies for the noble-gas sequence through Rn (Z = 86), the group-IIB atoms through Hg, and the ions of Ne isoelectronic sequence', Phys. Rev. A 50 (1994) 4733-4742.
8. T. KATO, Perturbation theory for linear operators, Grundlehren der Mathematischen Wissenschaften 132 (Springer, Berlin, 1966).
9. W. KUTZELNIGG, 'Relativistic one-electron Hamiltonians "for electrons only" and the variational treatment of the Dirac equation', Chemical Physics 225 (1997) 203-222.
10. J. J. LANDGREN and P. A. REJTO, 'An application of the maximum principle to the study of essential selfadjointness of Dirac operators. I', J. Math. Phys. 20 (1979) 2204-2211.
11. J. J. LANDGREN, P. A. REJTO and M. KLAUS, 'An application of the maximum principle to the study of essential selfadjointness of Dirac operators. II', J. Math. Phys. 21 (1981) 1210-1217.
12. E. H. LIEB, H. SIEDENTOP and J. P. SOLOVEJ, 'Stability and instability of relativistic electrons in classical electromagnetic fields', J. Statist. Phys. 89 (1997) 37-59.
13. E. H. LIEB, H. SIEDENTOP and J. P. SOLOVEJ, 'Stability of relativistic matter with magnetic fields', Phys. Rev. Lett. 79 (1997) 1785-1788.
14. M. REED and B. SIMON, Analysis of operators, Methods of Modern Mathematical Physics 4 (Academic Press, New York, 1978).
15. L. ROSENBERG and L. SPRUCH, ' Extremum principles for the determination of relativistic bound-state energies', Phys. Rev. A 34 (1986) 1720-1726.
16. U.-W. SCHMINCKE, 'Distinguished selfadjoint extensions of Dirac operators', Math. Z. 129 (1972) 335-349.
17. J. SUCHER, 'Foundations of the relativistic theory of many-electron atoms', Phys. Rev. A 22 (1980) 348-362.
18. J. D. TALMAN, 'Minimax principle for the Dirac equation', Phys. Rev. Lett. 57 (1986) 1091-1094.
19. B. THALLER, The Dirac equation, Texts and Monographs in Physics (Springer, Berlin, 1992).
20. C. TIX, 'Strict positivity of a relativistic Hamiltonian due to Brown and RavenhaU', Bull. London Math. Soc. 30 (1998) 283-290.