Quasi-classical asymptotics of local Riesz means for the Schrödinger operator in a moderate magnetic field
Annales de l'I.H.P. Physique théorique, Volume 62 (1995) no. 4, p. 325-360
@article{AIHPA_1995__62_4_325_0,
     author = {Sobolev, A. V.},
     title = {Quasi-classical asymptotics of local Riesz means for the Schr\"odinger operator in a moderate magnetic field},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     publisher = {Gauthier-Villars},
     volume = {62},
     number = {4},
     year = {1995},
     pages = {325-360},
     zbl = {0843.35024},
     mrnumber = {1343781},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1995__62_4_325_0}
}
Sobolev, A. V. Quasi-classical asymptotics of local Riesz means for the Schrödinger operator in a moderate magnetic field. Annales de l'I.H.P. Physique théorique, Volume 62 (1995) no. 4, pp. 325-360. http://www.numdam.org/item/AIHPA_1995__62_4_325_0/

[1] W.O. Amrein, A.-M. Boutet De Monvel-Berthier and V. Georgescu, Notes on The N-Body Problem, Part II, University of Geneve, preprint, Geneve, 1991. | MR 991005

[2] J. Avron, I. Herbst and B. Simon, Schrödinger operators with magnetic fields, I., Duke Math. J., Vol. 45 (4), 1978, pp. 847-883. | MR 518109 | Zbl 0399.35029

[3] C.L. Fefferman, V.J. Ivrii, L.A. Seco and I.M. Sigal, The energy asymptotics of large Coulomb systems, Lecture Notes in Physics, Vol. 403 (E. Balslev, ed.), Springer, Heidelberg, pp. 79-99. | MR 1181242 | Zbl 0834.47066

[4] B. Helffer and D. Robert, Calcul fonctionnel par la transformation de Mellin et opérateurs admissibles, J. Funct. Anal., Vol. 53, 1983, pp. 246-268. | MR 724029 | Zbl 0524.35103

[5] L. Hörmander, The Analysis of Linear Partial Differential Operators, I, Springer, Berlin, 1983. | MR 705278

[6] V. Ivrii and I.M. Sigal, Asymptotics of the ground state energies of Large Coulomb systems, Ann. of Math., Vol. 138, 1993, pp. 243-335. | MR 1240575 | Zbl 0789.35135

[7] V. Ivrii, Semiclassical Microlocal Analysis and Precise Spectral Asymptotics, École Polytechnique, Preprints, Palaiseau, 1991-1992.

[8] V. Ivrii, Estimates for the number of negative eigenvalues of the Schrödinger operator with a strong magnetic field, Soviet Math. Dokl., Vol. 36 (3), 1988, pp. 561-564. | MR 936071 | Zbl 0661.35066

[9] V. Ivrii, Estimates for the number of negative eigenvalues of the Schrödinger operator with singular potentials, Proc. Int. Congr. Math. Berkeley, 1986, pp. 1084-1093. | MR 922080 | Zbl 0719.47031

[10] L.D. Landau and E.M. Lifschitz, Quantum Mechanics - Nonrelativistic Theory, Pergamon Press, New York, 1965. | Zbl 0178.57901

[11] E.H. Lieb and B. Simon, The Thomas-Fermi theory of atoms, molecules and solids, Adv. in Math., Vol. 23, 1977, pp. 22-116. | MR 428944 | Zbl 0938.81568

[12] E.H. Lieb, J.P. Solovej and J. Yngvason, Heavy atoms in the strong magnetic field of a neutron star, Phys. Rev. Letters, Vol. 69, 1992, pp. 749-752.

[13] E.H. Lieb, J.P. Solovej and J. Yngvason, Asymptotics of heavy atoms in high magnetic fields: I. Lowest Landau band regions, Comm. Pure and Appl. Math. (to appear). | MR 1272387 | Zbl 0800.49041

[14] E.H. Lieb, J.P. Solovej and J. Yngvason, Asymptotics of heavy atoms in high magnetic fields: II. Semiclassical regions, Comm. Math. Phys., Vol. 161, 1994, pp. 77-124. | MR 1266071 | Zbl 0807.47058

[15] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. III, Academic Press, New York, 1979. | Zbl 0405.47007

[16] D. Robert, Autour de l'Approximation Semiclassique, Birkhäuser, Boston, 1987. | Zbl 0621.35001

[17] B. Simon, Lectures on Trace Ideals Methods, Cambridge University Press, London, 1979. | MR 541149

[18] A. Sobolev, The quasi-classical asymptotics of local Riesz means for the Schrödinger operator in a strong homogeneous magnetic field, Duke Math. J., Vol. 74 (2), 1994, pp. 319-429. | MR 1272980 | Zbl 0824.35151

[19] A. Sobolev, The sum of eigenvalues for the Schrödinger operator with Coulomb singularities in a homogeneous magnetic field, University of Nantes Preprint, 1993.