@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}, volume = {41}, year = {1984}, pages = {159-174}, mrnumber = {747200}, zbl = {0534.46053}, language = {en}, url = {http://dml.mathdoc.fr/item/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 41 (1984) pp. 159-174. http://gdmltest.u-ga.fr/item/AIHPA_1984__40_2_159_0/
[1] Endlichdimensionale analytische Störungstheorie, Akademie-Verlag, Berlin, 1972. | MR 634965 | Zbl 0303.47012
,[2] Dirac and Klein-Gordon Equations: Convergence of solutions in the nonrelativistic limit. Commun. Math. Phys., t. 79, 1981, p. 33-46. | MR 609226 | Zbl 0471.35024
and ,[3] Applications of a commutation formula. Duke Math. J., t. 45, 1978, p. 267-310. | MR 495676 | Zbl 0392.47013
,[4] On the Dirac theory of spin 1/2 particles and its non-relativistic limit. Phys. Rev., t. 78, 1950, p. 29-36. | Zbl 0039.22605
and ,[5] Spectral concentration in the nonrelativistic limit, Phys. Lett., 116 B, 1982, p. 155-157.
, and ,[6] First order relativistic corrections and spectral concentration. Adv. Appl. Math. (to appear). | MR 789851 | Zbl 0595.47007
, and ,[7] An efficient method for calculating relativistic corrections for spin-1/2 particles. Phys. Rev. Lett. (to appear).
, and ,[8] On the Friedrichs extension of ordinary differential operators with strongly singular potentials. Acta Phys. Austr., t. 51, 1979, p. 259-268. | MR 553603
and ,[9] On the self-adjointness of Dirac operators with anomalous magnetic moment (Caltech preprint, Pasadena, 1984).
, and ,[10] Nonrelativistic limit of relativistic quantum mechanics. Phys. Rev., t. D 24, 1981, p. 2127-2131. | MR 632521
and ,[11] On the nonrelativistic limit of the Dirac theory. Commun. Math. Phys., t. 40, 1975, p. 215-222. | MR 363275
,[12] Perturbation Theory for Linear Operators, 2nd ed., Springer-Verlag, New York/Berlin, 1980. | Zbl 0435.47001
,[13] Quantum Mechanics, vol. 2, North Holland, Amsterdam, 1970.
,[14] Linear Differential Operators, vol. 2, F. Ungar Publ., New York, 1968. | MR 262880 | Zbl 0227.34020
,[15] Relativistic potential scattering. J. Math. Phys., t. 4, 1963, p. 1048-1054. | MR 154563 | Zbl 0128.22004
,[16] Methods of Modern Mathematical Physics, vol. I: Functional Analysis, Academic Press, New York/London, 1972. | Zbl 0242.46001
and ,[17] Methods of Modern Mathematical Physics, vol. IV: Analysis of Operators, Academic Press, New York-San Francisco-London, 1978. | Zbl 0401.47001
and ,[18] On the nonrelativistic limits of the Klein-Gordon and Dirac equations, J. Math. Anal. Appl., t. 71, 1979, p. 36-47. | MR 545860 | Zbl 0427.35063
,[19] 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 0038.40603
,[20] 1/c Expansion of bound-state energies in QED, Nucl. Phys., t. B 196, 1982, p. 394-412. | MR 648057
,[21] On the relation between the eigenvalues in relativistic and non-relativistic quantum mechanics. Proc. Roy. Soc., t. A 266, 1962, p. 33-46. | MR 131598 | Zbl 0127.19004
,[22] Perturbation of pseudoresolvents and analyticity in 1/c of relativistic quantum mechanics. Commun. Math. Phys., t. 22, 1971, p. 27-43. | MR 300579 | Zbl 0212.15701
,[23] Existenz der Wellenoperatoren für eine allgemeine Klasse von Operatoren, Math. Z., t. 134, 1973, p. 255-274. | MR 336120 | Zbl 0258.47011
and ,[24] 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 0522.35008
,[25] Linear Operators in Hilbert Spaces, Springer-Verlag, New York/ Berlin, 1980. | MR 566954 | Zbl 0434.47001
,[26] Nonrelativistic limit of the Dirac theory, scattering theory, J. Fac. Sci. Univ. Tokyo, Sec. I A, t. 23, 1976, p. 517-523. | MR 434240 | Zbl 0341.47001
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