In this note, we study the scattering amplitude for the Schrödinger equation with constant magnetic field. We consider the case where the strengh of the magnetic field goes to infinity and we discuss the competition between the magnetic and the electrostatic effects.
@incollection{JEDP_2005____A8_0, author = {Laurent Michel}, title = {Scattering amplitude for the {Schr\"odinger} equation with strong magnetic field}, booktitle = {}, series = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {8}, pages = {1--17}, publisher = {Groupement de recherche 2434 du CNRS}, year = {2005}, doi = {10.5802/jedp.20}, mrnumber = {2352776}, language = {en}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.20/} }
TY - JOUR AU - Laurent Michel TI - Scattering amplitude for the Schrödinger equation with strong magnetic field JO - Journées équations aux dérivées partielles PY - 2005 SP - 1 EP - 17 PB - Groupement de recherche 2434 du CNRS UR - https://proceedings.centre-mersenne.org/articles/10.5802/jedp.20/ DO - 10.5802/jedp.20 LA - en ID - JEDP_2005____A8_0 ER -
%0 Journal Article %A Laurent Michel %T Scattering amplitude for the Schrödinger equation with strong magnetic field %J Journées équations aux dérivées partielles %D 2005 %P 1-17 %I Groupement de recherche 2434 du CNRS %U https://proceedings.centre-mersenne.org/articles/10.5802/jedp.20/ %R 10.5802/jedp.20 %G en %F JEDP_2005____A8_0
Laurent Michel. Scattering amplitude for the Schrödinger equation with strong magnetic field. Journées équations aux dérivées partielles (2005), article no. 8, 17 p. doi : 10.5802/jedp.20. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.20/
[1] S. Agmon Spectral properties of Schrödinger operators and scattering theory., Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser., Volume 2 (1975), pp. 151-218 | Numdam | MR | Zbl
[2] J. Avron; I. Herbst; B. Simon Schrödinger operators with magnetic fields. I. General interactions, Duke Math. J., Volume 45 (1978) no. 4, pp. 847-883 | MR | Zbl
[3] V. Bruneau; M. Dimassi Weak asymptotics of the spectral shift function in strong constant magnetic field (to appear)
[4] M. Dimassi Développements asymptotiques de l’opérateur de Schrödinger avec champ magnétique fort, Comm. Partial Differential Equations, Volume 26 (2001) no. 3-4, pp. 595-627 | MR | Zbl
[5] M. Dimassi; J. Sjöstrand Spectral asymptotics in the semi-classical limit, Cambridge University Press, Cambridge, 1999 | MR | Zbl
[6] C. Gérard Semiclassical resolvent estimates for two and three-body Schrödinger operators, Comm. Partial Differential Equations, Volume 15 (1990) no. 8, pp. 1161-1178 | MR | Zbl
[7] C. Gérard; A. Martinez Principe d’absorption limite pour des opérateurs de Schrödinger à longue portée, C. R. Acad. Sci. Paris Sér. I Math., Volume 306 (1988) no. 3, pp. 121-123 | MR | Zbl
[8] H. Isozaki; H. Kitada A remark on the microlocal resolvent estimates for two body Schrödinger operators, Publ. Res. Inst. Math. Sci., Volume 21 (1985) no. 5, pp. 889-910 | MR | Zbl
[9] V. P. Maslov; M. V. Fedoryuk Semi-classical approximation in quantum mechanics, Mathematical Physics and Applied Mathematics, Reidel Publishing company, 1981 | Zbl
[10] L. Michel Scattering amplitude for the Schrödinger equation with strong magnetic field and strong electric potential | MR | Zbl
[11] L. Michel Scattering amplitude and scattering phase for the Schrödinger equation with strong magnetic field, J. Math. Phys., Volume 46 (2005), pp. 043514, 18 pages
[12] E. Mourre Absence of singular continuous spectrum for certain selfadjoint operators, Comm. Math. Phys., Volume 78 (1980/81) no. 3, pp. 391-408 | MR | Zbl
[13] G. D. Raikov; M. Dimassi Spectral asymptotics for quantum Hamiltonians in strong magnetic fields, Cubo Mat. Educ., Volume 3 (2001) no. 2, pp. 317-391 | MR | Zbl
[14] M. Reed; B. Simon Methods of modern mathematical physics. IV., Academic Press, New York, 1978 (Analysis of operators) | MR | Zbl
[15] D. Robert; H. Tamura Asymptotic behavior of scattering amplitudes in semi-classical and low energy limits, Ann. Inst. Fourier (Grenoble), Volume 39 (1989) no. 1, pp. 155-192 | Numdam | MR | Zbl
[16] B. R. Vaĭnberg Quasiclassical approximation in stationary scattering problems, Funkcional. Anal. i Priložen., Volume 11 (1977) no. 4, p. 6-18, 96 | MR | Zbl
[17] X. P. Wang Barrier resonances in strong magnetic fields, Comm. Partial Differential Equations, Volume 17 (1992) no. 9-10, pp. 1539-1566 | MR | Zbl
Cited by Sources: