@article{AIHPA_1989__50_2_115_0,
author = {Nakamura, Shu},
title = {Scattering theory for the shape resonance model. I. Non-resonant energies},
journal = {Annales de l'I.H.P. Physique th\'eorique},
volume = {51},
year = {1989},
pages = {115-131},
mrnumber = {1002815},
zbl = {0686.35090},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPA_1989__50_2_115_0}
}
Nakamura, Shu. Scattering theory for the shape resonance model. I. Non-resonant energies. Annales de l'I.H.P. Physique théorique, Tome 51 (1989) pp. 115-131. http://gdmltest.u-ga.fr/item/AIHPA_1989__50_2_115_0/
[1] , Lectures on exponential decay of solutions of second order elliptic equations. Bounds on eigenfunctions of N-Body Schrödinger operators. Mathematical Notes. Princeton, N. J., Princeton Univ. Press, 1982. | MR 745286 | Zbl 0503.35001
[2] , , Perturbation theory for shape resonances and large barrior potentials. Commun. Math. Phys., t. 83, 1982, p. 151-170. | MR 649157 | Zbl 0494.34044
[3] , , , , The shape resonance. Commun. Math. Phys., t. 110, 1987, p. 215-236. | MR 887996 | Zbl 0629.47044
[4] , , , Convergent expansions for tunneling. Commun. Math. Phys., t. 92, 1983, p. 229-245. | MR 728868 | Zbl 0579.47050
[5] , , , On the shape resonance. Springer lecture notes in physics, 1984, t. 211, p. 64-77. | MR 777332
[6] , Semiclassical quantum mechanics. I: the h → 0 limit for coherent states. Commun. Math. Phys., t. 71, 1980, p. 77-93. | MR 556903
[7] , On the rate of eigenvalue degeneracy. Commun. Math. Phys., t. 60, 1978, p. 73-95. | MR 486764 | Zbl 0395.34023
[8] , Double wells. Commun. Math. Phys., t. 75, 1980, p. 239-261. | MR 581948 | Zbl 0445.35036
[9] , , Multiple wells in the semi-classical limit. I. Commun. in PDE, t. 9, 1985, p. 337-369. | Zbl 0546.35053
[10] , , Resonances en limite semi-classique. Preprint.
[11] , Scattering theory with two Hilbert spaces. J. Funct. Anal., t. 1, 1967, p. 342- 369. | MR 220097 | Zbl 0171.12303
[12] , , The abstract theory of scattering. Rocky Mountain J. Math., t. 1, 1971, p. 127-171. | MR 385604 | Zbl 0241.47005
[13] , On the absence of resonances for Schrödinger operators with non-trapping potentials in the classical limit. Commun. Math. Phys., 1986, t. 106, p. 485-494. | MR 859823 | Zbl 0651.47007
[14] , Scattering theory for differential operators. I.-II. J. Math. Soc. Japan, t. 25, 1973, p. 75-104 ; 222-234. | Zbl 0245.47006
[15] , Absolute continuity of positive spectrum for Schrödinger operators with long-range potentials. J. Funct. Anal., t. 12, 1973, p. 30-54. | MR 342880 | Zbl 0246.47017
[16] , , Methods of modern mathematical physics. I-IV. New York, New York, San Francisco, London, Academic Press, 1972-1979. | MR 751959
[17] , , Semi-classical bounds for resolvents of Schrödinger operators and asymptotics for scattering phase. Commun. in PDE, t. 9, 1984, p. 1017- 1058. | MR 755930 | Zbl 0561.35021
[18] , , Semi-classical estimates for resolvents and asymptotics for total scattering cross-sections. Preprint.
[19] , The semiclassical limit of quantum dynamics. I: Time evolution; II: Scattering theory. Preprints. | MR 927028
[20] , Semiclassical analysis of low lying eigenvalues. II. Tunneling. Ann. Math., t. 120, 1984, p. 89-118. | MR 750717 | Zbl 0626.35070
[21] , Semiclassical analysis of low lying eigenvalues. IV. Flea of elephants. J. Funct. Anal., t. 63, 1985, p. 123-136. | MR 795520 | Zbl 0652.35090
[22] , Quasi-classical approximation in stationary scattering problems, Funct. Anal. Appl., t. 11, 1977, p. 6-18.
[23] , The eikonal approximation and the asymptotics of the total cross-section for the Schrödinger equation. Ann. Inst. Henri Poincaré, t. 44, 1986, p. 397- 425. | Numdam | MR 850898 | Zbl 0608.35054
[24] , The quasi-classical limit of scattering amplitude, Finite range potentials. Springer lecture notes in math., t. 1159, 1985, p. 242-263. | MR 824991 | Zbl 0591.35079
[25] , The quasi-classical limit of scattering amplitude, L2-approach for short range potentials. Japan. J. Math., t. 13, 1987, p. 77-126. | MR 914315 | Zbl 0648.35067
[26] , Private communication.
[27] , , , On the location of resonances for Schrodinger operators in the semiclassical limit : Resonance free domains. To appear in J. Math. Anal. Appl. | Zbl 0629.47043
[28] , , , On the location of resonances for Schrödinger operators in the semiclassical limit: II. Barrier top resonances. Commun. in PDE, t. 12, 1987, p. 201-222. | MR 876987 | Zbl 0622.47047