Bohm Aharonov effects for bounded states in the case of systems
Hebbar, O.
Annales de l'I.H.P. Physique théorique, Tome 61 (1994), p. 489-500 / Harvested from Numdam
Publié le : 1994-01-01
@article{AIHPA_1994__60_4_489_0,
     author = {Hebbar, O.},
     title = {Bohm Aharonov effects for bounded states in the case of systems},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {61},
     year = {1994},
     pages = {489-500},
     mrnumber = {1288589},
     zbl = {0811.53021},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1994__60_4_489_0}
}
Hebbar, O. Bohm Aharonov effects for bounded states in the case of systems. Annales de l'I.H.P. Physique théorique, Tome 61 (1994) pp. 489-500. http://gdmltest.u-ga.fr/item/AIHPA_1994__60_4_489_0/

[1] J. Avron, I. Herbst and B. Simon, Schrödinger Operators with Magnetic Fields. I. General Interactions, Duke Math. Journal, 45, 1978, pp. 847-884. | MR 518109 | Zbl 0399.35029

[2] B. Doubrovine, S. Novikov and A. Fomenko, Géométrie contemporaine. Méthodes et applications, Éditions Mir, Moscou, 1979. | Zbl 0502.53002

[3] D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, 1977. | MR 473443 | Zbl 0361.35003

[4] O. Hebbar, Effet d'Aharonov-Bohm pour un état borné dans le cas des systèmes, Thèse de Doctorat à l'Université de Nantes (France), 1992.

[5] B. Helffer, Effet d'Aharonov-Bohm sur un état borné de l'équation de Schrödinger, Commun. Math. Phys., 119, 1988, 315-329. | MR 968700 | Zbl 0702.35186

[6] H. Hess, R. Schrader and D.A. Uhlenbrock, Domination of Semigroups and Generalization of Kato's Inequality, Duke Math. Journal, Vol. 44, 4, 1977. | MR 458243 | Zbl 0379.47028

[7] H. Hess, R. Schrader and D.A. Uhlenbrock, Kato's Inequality and the Spectral Distribution of Laplacian on Compact Riemannian Manifolds, J. Diff. Geometry, 15, 1980, pp. 27-37. | MR 602436 | Zbl 0442.58032

[8] R. Kuwabara, On Spectra of the Laplacian on Vector Bundles, J. Math. Tokushima Univ., 4, Vol. 16, 1982, pp. 1-23. | MR 691445 | Zbl 0504.53039

[9] R. Lavine and M. O'Caroll, Ground State Properties and Lower Bounds on Energy Levels of a Particle in a Uniform Magnetic Field and External Potential, J. Math. Phys., Vol. 18, 1977, pp. 1908-1912. | MR 456039

[10] S. Manabe and I. Shigekawa, A Comparison Theorem for Eigenvalues of the Covariant Laplacian, J. Funct. Anal., Vol. 94, 1990, pp. 349-357. | MR 1081648 | Zbl 0716.58030

[11] M. Reed and B. Simon, Methods of modern mathematical physics, IV, New York, Academic press, 1978. | MR 751959 | Zbl 0401.47001

[12] I. Shigekawa, Eigenvalue Problems for the Schrödinger Operator with the Magnetic Field on a Compact Riemannian Manifold, J. Funct. Anal., 75, 1987, pp 92-127. | MR 911202 | Zbl 0629.58023

[13] R.O. Wells, Differential Analysis on Complex Manifolds, Grad. Texts. Math., Vol. 65, Springer-Verlag, 1979. | Zbl 0435.32004