Perturbation of pseudoresolvents and analyticity in 1/c in relativistic quantum mechanics
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The analytic functional calculus, relatively bounded and analytic perturbations of pseudoresolvents have been studied. As an application, the nonrelativistic limit of the Dirac and Klein-Gordon operator in the presence of an external static field has been considered. It has been proved that the resolvents of these operators have only a removable singularity atc=∞. This implies the analyticity atc=∞ of the eigenvalues and eigenvectors corresponding to the bound states of the mentioned operators.
KeywordsNeural Network Statistical Physic Complex System Quantum Mechanic Static Field
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- 1.Dunford, N., Schwartz, J.: Linear operators. New York: Interscience 1958.Google Scholar
- 2.Hille, E., Phillips, R.: Functional analysis and semigroups (Russian translation). I. L. Moskva, 1962.Google Scholar
- 3.Kato, T.: Perturbation theory for linear operators. Heidelberg, New York: Springer 1966.Google Scholar
- 4.Prosser, R. T.: J. Math. Phys.4, 1048 (1963).Google Scholar
- 5.Saphar, P.: Ann. Sci. Ec. Norm. Sup.82, 205 (1965).Google Scholar
- 6.Titchmarsh, E.: Proc. Roy. Soc. A266, 33 (1962).Google Scholar
- 7.Veselić, K.: Nucl. Phys. A147, 215 (1970).Google Scholar
- 8.-- Thesis, University of Zagreb, 1970.Google Scholar