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Schoene, Andrew Y.

On the nonrelativistic limits of the Klein-Gordon and Dirac equations. (English) Zbl 0427.35063

J. Math. Anal. Appl. 71, 36-47 (1979).
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Cited in 29 Documents

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
35B25 Singular perturbations in context of PDEs
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
83C50 Electromagnetic fields in general relativity and gravitational theory

Keywords:

Klein-Gordon and Dirac equations; relativistic quantum mechanics; nonrelativistic limits; limiting behavior; electrostatic potentials with Coulomb type singularities

Citations:

Zbl 0219.47034; Zbl 0203.40101
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Full Text: DOI

References:

[1] Friedman, A., Singular perturbations for the Cauchy problem and for boundary value problems, J. Differential Equations, 5, 226-261 (1969) · Zbl 0182.42301
[2] Kato, T., Some mathematical problems in quantum mechanics, Suppl. Progr. Theoret. Phys., 40, 3-19 (1967)
[3] Kato, T., Perturbation Theory for Linear Operators (1966), Springer-Verlag: Springer-Verlag Berlin · Zbl 0148.12601
[4] O’Malley, R. E., Topics in singular perturbations, (Busemann, H., Advances in Mathematics, Vol. 2 (1968), Academic Press: Academic Press New York), 365-470, Fasc. 4 · Zbl 0203.40101
[5] Riesz, F.; -Nagy, B. Sz, Functional Analysis (1955), Ungar: Ungar New York
[6] Schiff, L. I., Quantum Mechanics (1968), McGraw-Hill: McGraw-Hill New York · Zbl 0068.40202
[7] Schoene, A. Y., Semi-groups and a class of singular perturbation problems, Indiana Univ. Math. J., 20, 247-263 (1970) · Zbl 0219.47034
[8] Smoller, J. A., Singular perturbations of Cauchy’s problem, Comm. Pure Appl. Math., 18, 665-677 (1965) · Zbl 0151.20302
[9] Zlamal, M., On a Singular Perturbation Problem Concerning Hyperbolic Equations, (Institute for Fluid Dynamics and Applied Mathematics, Lecture Series No. 45 (1965), Univ. of Maryland: Univ. of Maryland College Park) · Zbl 0161.30303
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