A rigorous approach to relativistic corrections of bound state energies for spin-1/2 particles

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1. [1] H. Baumgärtel, Endlichdimensionale analytische Störungstheorie, Akademie-Verlag, Berlin, 1972. Zbl0303.47012MR634965
2. [2] R.J. Cirincione and P.R. Chernoff, Dirac and Klein-Gordon Equations: Convergence of solutions in the nonrelativistic limit. Commun. Math. Phys., t. 79, 1981, p. 33-46. Zbl0471.35024MR609226
3. [3] P.A. Deift, Applications of a commutation formula. Duke Math. J., t. 45, 1978, p. 267-310. Zbl0392.47013MR495676
4. [4] L.L. Foldy and S.A. Wouthuysen, On the Dirac theory of spin 1/2 particles and its non-relativistic limit. Phys. Rev., t. 78, 1950, p. 29-36. Zbl0039.22605
5. [5] F. Gesztesy, H. Grosse and B. Thaller, Spectral concentration in the nonrelativistic limit, Phys. Lett., 116 B, 1982, p. 155-157. 
6. [6] F. Gesztesy, H. Grosse and B. Thaller, First order relativistic corrections and spectral concentration. Adv. Appl. Math. (to appear). Zbl0595.47007MR789851
7. [7] F. Gesztesy, H. Grosse and B. Thaller, An efficient method for calculating relativistic corrections for spin-1/2 particles. Phys. Rev. Lett. (to appear). Zbl0534.46053
8. [8] F. Gesztesy and L. Pittner, On the Friedrichs extension of ordinary differential operators with strongly singular potentials. Acta Phys. Austr., t. 51, 1979, p. 259-268. MR553603
9. [9] F. Gesztesy, B. Simon and B. Thaller, On the self-adjointness of Dirac operators with anomalous magnetic moment (Caltech preprint, Pasadena, 1984). 
10. [10] L.P. Horwitz and F.C. Rotbart, Nonrelativistic limit of relativistic quantum mechanics. Phys. Rev., t. D 24, 1981, p. 2127-2131. MR632521
11. [11] W. Hunziker, On the nonrelativistic limit of the Dirac theory. Commun. Math. Phys., t. 40, 1975, p. 215-222. MR363275
12. [12] T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Springer-Verlag, New York/Berlin, 1980. Zbl0435.47001
13. [13] A. Messiah, Quantum Mechanics, vol. 2, North Holland, Amsterdam, 1970. 
14. [14] M.A. Naimark, Linear Differential Operators, vol. 2, F. Ungar Publ., New York, 1968. Zbl0227.34020MR262880
15. [15] R.T. Prosser, Relativistic potential scattering. J. Math. Phys., t. 4, 1963, p. 1048-1054. Zbl0128.22004MR154563
16. [16] M. Reed and B. Simon, Methods of Modern Mathematical Physics, vol. I: Functional Analysis, Academic Press, New York/London, 1972. Zbl0242.46001
17. [17] M. Reed and B. Simon, Methods of Modern Mathematical Physics, vol. IV: Analysis of Operators, Academic Press, New York-San Francisco-London, 1978. Zbl0401.47001
18. [18] A.Y. Schoene, On the nonrelativistic limits of the Klein-Gordon and Dirac equations, J. Math. Anal. Appl., t. 71, 1979, p. 36-47. Zbl0427.35063MR545860
19. [19] G.L. Sewell, An appropriate relation between the energy levels of a particle in a field of given potential energy, calculated in the relativistic and non-relativistic theories. Proc. Cambridge Phil. Soc., t. 45, 1949, p. 631-637. Zbl0038.40603
20. [20] O. Steinmann, 1/c Expansion of bound-state energies in QED, Nucl. Phys., t. B 196, 1982, p. 394-412. MR648057
21. [21] E.C. Titchmarsh, On the relation between the eigenvalues in relativistic and non-relativistic quantum mechanics. Proc. Roy. Soc., t. A 266, 1962, p. 33-46. Zbl0127.19004MR131598
22. [22] K. Veselić, Perturbation of pseudoresolvents and analyticity in 1/c of relativistic quantum mechanics. Commun. Math. Phys., t. 22, 1971, p. 27-43. Zbl0212.15701MR300579
23. [23] K. Veselić and J. Weidmann, Existenz der Wellenoperatoren für eine allgemeine Klasse von Operatoren, Math. Z., t. 134, 1973, p. 255-274. Zbl0258.47011MR336120
24. [24] K. Veselić, On the non-relativistic limit of the bound states of the Klein-Gordon equation. J. Math. Anal. Appl., t. 96, 1983, p. 63-84. Zbl0522.35008
25. [25] J. Weidmann, Linear Operators in Hilbert Spaces, Springer-Verlag, New York/ Berlin, 1980. Zbl0434.47001MR566954
26. [26] K. Yajima, Nonrelativistic limit of the Dirac theory, scattering theory, J. Fac. Sci. Univ. Tokyo, Sec. I A, t. 23, 1976, p. 517-523. Zbl0341.47001MR434240

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