Semiclassical and weak-magnetic-field eigenvalue asymptotics for the Schrödinger operator with electromagnetic potential
Annales de l'I.H.P. Physique théorique, Tome 61 (1994) no. 2, pp. 163-188. 
@article{AIHPA_1994__61_2_163_0,
     author = {Raikov, George D.},
     title = {Semiclassical and weak-magnetic-field eigenvalue asymptotics for the {Schr\"odinger} operator with electromagnetic potential},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {163--188},
     publisher = {Gauthier-Villars},
     volume = {61},
     number = {2},
     year = {1994},
     mrnumber = {1311063},
     zbl = {0812.35113},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1994__61_2_163_0/}
}
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Raikov, George D. Semiclassical and weak-magnetic-field eigenvalue asymptotics for the Schrödinger operator with electromagnetic potential. Annales de l'I.H.P. Physique théorique, Tome 61 (1994) no. 2, pp. 163-188. http://www.numdam.org/item/AIHPA_1994__61_2_163_0/

[Ale] A.B. Alekseev, On the spectral asymptotics of differential operators with polynomial occurrence of a small parameter, Probl. Mat. Fiz., Vol. 8, 1976, pp.3-15 (in Russian). | MR

[Av.Her.Sim 1] J. Avron, I. Herbst and B. Simon, Schrödinger operators with magnetic fields. I. General interactions, Duke Math. J., Vol. 45, 1978, pp. 847-883. | MR | Zbl

[Av.Her.Sim 2] J. Avron, I. Herbst and B. Simon, Schrödinger operators with magnetic fields. III. Atoms in homogeneous magnetic field, Commun. Math. Phys., Vol. 79, 1981, pp. 529-572. | MR | Zbl

[Bir] M.S. Birman, On the spectrum of singular boundary value problems, AMS Translations, (2), Vol. 53, 1966, pp. 23-80. | Zbl

[Bir.Sol 1] M.S. Birman and M.Z. Solomjak, Estimates of the singular numbers of integral operators, Russian Math. Surveys, Vol. 32, 1977, pp. 15-89. | MR | Zbl

[Bir.Sol 2] M.S. Birman and M.Z. Solomjak, Quantitative analysis in Sobolev imbedding theorems and applications to spectral theory, AMS Translations (2), Vol. 114, 1980. | Zbl

[Bir.Sol 3] M.S. Birman and M.Z. Solomjak, Spectral Theory of Selfadjoint Operators in Hilbert Space, D. REIDEL, Dordrecht, 1987. | Zbl

[CdV] Y. Colin De Verdière, L'asymptotique de Weyl pour les bouteilles magnétiques, Comm. Math. Phys., Vol. 105, 1986, pp. 327-335. | MR | Zbl

[Com.Sch.Sei] J.M. Combes, R. Schrader and R. Seiler, Classical bounds and limits for energy distributions of Hamiltonian operators in electromagnetic fields, Ann. Physics, Vol. 111, 1978, pp. 1-18. | MR

[Cy.Fr.Ki.Sim] H.L. Cycon, R.G. Froese, W. Kirsch and B. Simon, Schrödinger operators with Application to Quantum Mechanics and Global Geometry. Springer, Berlin, 1987. | MR | Zbl

[Dau.Rob] M. Dauge and D. Robert, Weyl's formula for a class of pseudodifferential operators of negative order on L2 (Rn), Lect. Notes Mah., Vol. 1256, 1987, pp. 91-122. | MR | Zbl

[Gre.Sze] U. Grenander and G. Szegö, Toeplitz Forms and Their Applications, University of California Press, Berkeley-Los Angeles, 1958. | MR | Zbl

[Hel.Sjö 1] B. Helffer and J. Sjöstrand, Équation de Schrödinger avec champ magnétique et équation de Harper, II. Approximation champ magnétique faible: substitution de Peierls. In: Schrödinger operators, Lect. Notes Phys., Vol. 345, 1988, pp. 138-191.

[Hel.Sjö 2] B. Helffer and J. Sjöstrand, On the link between the Schrödinger operator with magnetic field and Harper's equation, In: Proceedings of Symp. Part. Diff. Equ., HOLZHAU, 1988. Teubner-Texte zur Mathematik, Vol. 112, 1989, pp. 139-156. | Zbl

[Ivr 1] V.Ya. Ivrii, Estimations pour le nombre de valeurs propres négatives de l'opérateur de Schrödinger avec potentiels singuliers, C. R. Acad. Sci. Paris, Sér. I, Vol. 302, 1986, pp. 467-470. | MR | Zbl

[Ivr 2] V.Ya. Ivrii, Estimates of the number of negative eigenvalues of the Schrödinger operator with a strong magnetic field, Soviet Math. Dokl., Vol. 36, 1988, pp. 561-564. | MR | Zbl

[Ivr 3] V.Ya. Ivrii, Sharp spectral asymptotics for the two-dimensional Schrödinger operator with a strong magnetic field, Soviet Math. Dokl., Vol. 39, 1989, pp. 437-441. | MR | Zbl

[Ivr 4] V.Ya. Ivrii, Semiclassical microlocal analysis and precise spectral asymptotics, Preprints 1-9, École Polytechnique, 1990-1992.

[Lei] H. Leinfelder, Gauge invariance of Schrödinger operators and related spectral properties, J. Opt. Theory, Vol. 9, 1983, pp. 163-179. | MR | Zbl

[Rai 1] G.D. Raikov, Spectral asymptotics for the Schrödinger operator with potential which steadies at infinity, Comm. Math. Phys., Vol. 124, 1989, pp. 665-685. | MR | Zbl

[Rai 2] G.D. Raikov, Eigenvalue asymptotics for the Schrödinger operator with homogeneous magnetic potential and decreasing electric potential. I. Behaviour near the essential spectrum tips, Comm. P.D.E., Vol. 15, 1990, pp. 407-434. | MR | Zbl

[Rai 3] G.D. Raikov, Strong electric field eigenvalue asymptotics for the Schrödinger operator with electromagnetic potential, Letters Math. Phys., Vol. 21, 1991, pp. 41-49. | MR | Zbl

[Rai 4] G.D. Raikov, Semiclassical and weak-magnetic-field eigenvalue asymptotics for the Schrödinger operator with electromagnetic potential, C. R. Acad. Sci. Bulg., Vol. 44, 1991, No. 1, pp.15-18. | MR | Zbl

[Ree.Sim] M. Reed and B. Simon, Methods of Modem Mathematical Physics. IV. Analysis of Operators, Academic Press, London, 1978. | Zbl

[Roz] G.V. Rozenbljum, An asymptotic of the negative discrete spectrum of the Schrödinger operator, Math. Notes U.S.S.R., Vol. 21, 1977, pp. 222-227. | MR | Zbl

[Sim] B. Simon, Functional Integration and Quantum Physics, Academic Press, London, 1979. | MR | Zbl

[Tam] H. Tamura, Asymptotic distribution of eigenvalues for Schrödinger operators with homogeneous magnetic fields, Osaka J. Math., Vol.25, 1988, pp. 633- 647. | MR | Zbl