no. 2
Scattering theory for the shape resonance model. I. Non-resonant energies
Annales de l'I.H.P. Physique théorique, Tome 50 (1989) no. 2, pp. 115-131.
partie suivante Scattering theory for the shape resonance model. II. Resonance scattering 
@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},
     pages = {115--131},
     publisher = {Gauthier-Villars},
     volume = {50},
     number = {2},
     year = {1989},
     mrnumber = {1002815},
     zbl = {0686.35090},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1989__50_2_115_0/}
}
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Nakamura, Shu. Scattering theory for the shape resonance model. I. Non-resonant energies. Annales de l'I.H.P. Physique théorique, Tome 50 (1989) no. 2, pp. 115-131. http://www.numdam.org/item/AIHPA_1989__50_2_115_0/

[1] S. Agmon, 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 | Zbl

[2] M. Ashbaugh, E. Harrell, Perturbation theory for shape resonances and large barrior potentials. Commun. Math. Phys., t. 83, 1982, p. 151-170. | MR | Zbl

[3] J.M. Combes, P. Duclos, M. Klein, R. Seiler, The shape resonance. Commun. Math. Phys., t. 110, 1987, p. 215-236. | MR | Zbl

[4] J.M. Combes, P. Duclos, R. Seiler, Convergent expansions for tunneling. Commun. Math. Phys., t. 92, 1983, p. 229-245. | MR | Zbl

[5] J.M. Combes, P. Duclos, R. Seiler, On the shape resonance. Springer lecture notes in physics, 1984, t. 211, p. 64-77. | MR

[6] G. Hagedorn, Semiclassical quantum mechanics. I: the h → 0 limit for coherent states. Commun. Math. Phys., t. 71, 1980, p. 77-93. | MR

[7] E. Harrell, On the rate of eigenvalue degeneracy. Commun. Math. Phys., t. 60, 1978, p. 73-95. | MR | Zbl

[8] E. Harrell, Double wells. Commun. Math. Phys., t. 75, 1980, p. 239-261. | MR | Zbl

[9] B. Helffer, J. Sjöstrand, Multiple wells in the semi-classical limit. I. Commun. in PDE, t. 9, 1985, p. 337-369. | Zbl

[10] B. Helffer, J. Sjöstrand, Resonances en limite semi-classique. Preprint.

[11] T. Kato, Scattering theory with two Hilbert spaces. J. Funct. Anal., t. 1, 1967, p. 342- 369. | MR | Zbl

[12] T. Kato, S.T. Kuroda, The abstract theory of scattering. Rocky Mountain J. Math., t. 1, 1971, p. 127-171. | MR | Zbl

[13] M. Klein, 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 | Zbl

[14] S.T. Kuroda, Scattering theory for differential operators. I.-II. J. Math. Soc. Japan, t. 25, 1973, p. 75-104 ; 222-234. | Zbl

[15] R. Lavine, Absolute continuity of positive spectrum for Schrödinger operators with long-range potentials. J. Funct. Anal., t. 12, 1973, p. 30-54. | MR | Zbl

[16] M. Reed, B. Simon, Methods of modern mathematical physics. I-IV. New York, New York, San Francisco, London, Academic Press, 1972-1979. | MR

[17] D. Robert, H. Tamura, Semi-classical bounds for resolvents of Schrödinger operators and asymptotics for scattering phase. Commun. in PDE, t. 9, 1984, p. 1017- 1058. | MR | Zbl

[18] D. Robert, H. Tamura, Semi-classical estimates for resolvents and asymptotics for total scattering cross-sections. Preprint.

[19] S.L. Robinson, The semiclassical limit of quantum dynamics. I: Time evolution; II: Scattering theory. Preprints. | MR

[20] B. Simon, Semiclassical analysis of low lying eigenvalues. II. Tunneling. Ann. Math., t. 120, 1984, p. 89-118. | MR | Zbl

[21] B. Simon, Semiclassical analysis of low lying eigenvalues. IV. Flea of elephants. J. Funct. Anal., t. 63, 1985, p. 123-136. | MR | Zbl

[22] B.R. Vainverg, Quasi-classical approximation in stationary scattering problems, Funct. Anal. Appl., t. 11, 1977, p. 6-18.

[23] D.R. Yafaev, 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 | Zbl

[24] K. Yajima, The quasi-classical limit of scattering amplitude, Finite range potentials. Springer lecture notes in math., t. 1159, 1985, p. 242-263. | MR | Zbl

[25] K. Yajima, The quasi-classical limit of scattering amplitude, L2-approach for short range potentials. Japan. J. Math., t. 13, 1987, p. 77-126. | MR | Zbl

[26] K. Yajima, Private communication.

[27] P. Briet, J.M. Combes, P. Duclos, On the location of resonances for Schrodinger operators in the semiclassical limit : Resonance free domains. To appear in J. Math. Anal. Appl. | Zbl

[28] P. Briet, J.M. Combes, P. Duclos, 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 | Zbl