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Approximation des valeurs propres de certaines perturbations singulières et application à l’opérateur de Dirac. (Approximation of the eigenvalues of some singular perturbations and application to the Dirac operator). (French) Zbl 0755.35106
In this article, the authors establish some results on the approximation of discrete eigenvalues. As an application, they obtain the asymptotic behavior of the splitting of the first four eigenvalues related to the double-well problem for the Dirac operator, with or without magnetic field, in the semiclassical limit and the relativistic one. This gives complements to Xue Ping Wang [Ann. Inst. Henri Poincaré. Phys. Théor., Vol. 43, 269-319 (1985; Zbl 0614.35074)].
Reviewer: B.Helffer (Paris)

MSC:
35Q40 PDEs in connection with quantum mechanics
35P15 Estimates of eigenvalues in context of PDEs
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
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