A rigorous approach to relativistic corrections of bound state energies for spin-1/2 particles
Annales de l'I.H.P. Physique théorique, Tome 40 (1984) no. 2, pp. 159-174.
@article{AIHPA_1984__40_2_159_0,
     author = {Gesztesy, F. and Grosse, H. and Thaller, B.},
     title = {A rigorous approach to relativistic corrections of bound state energies for spin-1/2 particles},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {159--174},
     publisher = {Gauthier-Villars},
     volume = {40},
     number = {2},
     year = {1984},
     mrnumber = {747200},
     zbl = {0534.46053},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1984__40_2_159_0/}
}
TY  - JOUR
AU  - Gesztesy, F.
AU  - Grosse, H.
AU  - Thaller, B.
TI  - A rigorous approach to relativistic corrections of bound state energies for spin-1/2 particles
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1984
SP  - 159
EP  - 174
VL  - 40
IS  - 2
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1984__40_2_159_0/
LA  - en
ID  - AIHPA_1984__40_2_159_0
ER  - 
%0 Journal Article
%A Gesztesy, F.
%A Grosse, H.
%A Thaller, B.
%T A rigorous approach to relativistic corrections of bound state energies for spin-1/2 particles
%J Annales de l'I.H.P. Physique théorique
%D 1984
%P 159-174
%V 40
%N 2
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1984__40_2_159_0/
%G en
%F AIHPA_1984__40_2_159_0
Gesztesy, F.; Grosse, H.; Thaller, B. A rigorous approach to relativistic corrections of bound state energies for spin-1/2 particles. Annales de l'I.H.P. Physique théorique, Tome 40 (1984) no. 2, pp. 159-174. http://www.numdam.org/item/AIHPA_1984__40_2_159_0/

[1] H. Baumgärtel, Endlichdimensionale analytische Störungstheorie, Akademie-Verlag, Berlin, 1972. | MR | Zbl

[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. | MR | Zbl

[3] P.A. Deift, Applications of a commutation formula. Duke Math. J., t. 45, 1978, p. 267-310. | MR | Zbl

[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. | Zbl

[5] F. Gesztesy, H. Grosse and B. Thaller, Spectral concentration in the nonrelativistic limit, Phys. Lett., 116 B, 1982, p. 155-157.

[6] F. Gesztesy, H. Grosse and B. Thaller, First order relativistic corrections and spectral concentration. Adv. Appl. Math. (to appear). | MR | Zbl

[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).

[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. | MR

[9] F. Gesztesy, B. Simon and B. Thaller, On the self-adjointness of Dirac operators with anomalous magnetic moment (Caltech preprint, Pasadena, 1984).

[10] L.P. Horwitz and F.C. Rotbart, Nonrelativistic limit of relativistic quantum mechanics. Phys. Rev., t. D 24, 1981, p. 2127-2131. | MR

[11] W. Hunziker, On the nonrelativistic limit of the Dirac theory. Commun. Math. Phys., t. 40, 1975, p. 215-222. | MR

[12] T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Springer-Verlag, New York/Berlin, 1980. | Zbl

[13] A. Messiah, Quantum Mechanics, vol. 2, North Holland, Amsterdam, 1970.

[14] M.A. Naimark, Linear Differential Operators, vol. 2, F. Ungar Publ., New York, 1968. | MR | Zbl

[15] R.T. Prosser, Relativistic potential scattering. J. Math. Phys., t. 4, 1963, p. 1048-1054. | MR | Zbl

[16] M. Reed and B. Simon, Methods of Modern Mathematical Physics, vol. I: Functional Analysis, Academic Press, New York/London, 1972. | Zbl

[17] M. Reed and B. Simon, Methods of Modern Mathematical Physics, vol. IV: Analysis of Operators, Academic Press, New York-San Francisco-London, 1978. | Zbl

[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. | MR | Zbl

[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. | Zbl

[20] O. Steinmann, 1/c Expansion of bound-state energies in QED, Nucl. Phys., t. B 196, 1982, p. 394-412. | MR

[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. | MR | Zbl

[22] K. Veselić, Perturbation of pseudoresolvents and analyticity in 1/c of relativistic quantum mechanics. Commun. Math. Phys., t. 22, 1971, p. 27-43. | MR | Zbl

[23] K. Veselić and J. Weidmann, Existenz der Wellenoperatoren für eine allgemeine Klasse von Operatoren, Math. Z., t. 134, 1973, p. 255-274. | MR | Zbl

[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. | Zbl

[25] J. Weidmann, Linear Operators in Hilbert Spaces, Springer-Verlag, New York/ Berlin, 1980. | MR | Zbl

[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. | MR | Zbl