A semi-classical picture of quantum scattering

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1. [1] R. ABRAHAM and J. E. MARSDEN, Foundation of Mechanics, Addison Wesley, 1985. 
2. [2] W. O. AMREIN, J. M. JAUCH and K. B. SINHA, Scattering Theory in Quantum Mechanics, W. A. Benjamin, 1977. Zbl0376.47001MR58 #14631
3. [3] F. A. BEREZIN and M. A. SHUBIN, The Schrödinger Equation, volume 66 of Mathematics and its Applications, Kluwer Academic Publishers, 1991. Zbl0749.35001MR93i:81001
4. [4] J. M. BONY, Second Microlocalization and Propagation of Singularities for Semi-linear Hyperbolic Equations (Hyperbolic Equations and Related Topics, Mizohata ed. Kinokuya, 1986, pp. 11-49). Zbl0669.35073MR89e:35099
5. [5] J. M. BONY and J. Y. CHEMIN, Espaces fonctionnels associés au calcul de Weyl-Hörmander (Bull. Soc. Math. France, 1994, pp. 77-118). Zbl0798.35172MR95a:35152
6. [6] J. M. BONY and N. LERNER, Quantification asymptotique et microlocalisation d'ordre supérieur I (Ann. Scient. Ec. Norm. Sup., 4e série, Vol. 22, 1989, pp. 377-433). Zbl0753.35005MR90k:35276
7. [7] O. BRATELLI and D. ROBINSON, Operator Algebras and Quantum Statistical Physics, Springer-Verlag, 1979-1981. 
8. [8] C. COHEN-TANNOUDJI, B. DIU and F. LALOË, Mécanique Quantique, Hermann, 1973. 
9. [9] P. DEIFT and E. TRUBOWITZ, Inverse Scattering on the Line (Comm. on Pure and Applied Math., Vol. 32, 1979, pp. 121-251). Zbl0388.34005MR80e:34011
10. [10] J. DEREZINSKI and C. GÉRARD, Asymptotic Completeness of N-Particles Systems, Springer Verlag, to appear. Zbl0784.47055
11. [11] J. DIXMIER, Les C*-algèbres et leurs représentations, Gauthier-Villars, 1964. Zbl0152.32902MR30 #1404
12. [12] J. D. DOLLARD, Scattering into Cones 1 : Potential Scattering (Commun. in Math. Phys., Vol. 12, 1969, pp. 193-203). 
13. [13] J. J. DUISTERMAAT, Oscillatory Integrals, Lagrange Immersions and Unfolding of Singularities (Comm. on Pure and Applied Math., Vol. 27, 1974, pp. 207-281). Zbl0285.35010MR53 #9306
14. [14] M. V. FEDORYUK and V. P. MASLOV, Semi-Classical Approximation in Quantum Mechanics, Reidel Publishing Company, 1985. Zbl0458.58001
15. [15] C. FERMANIAN-KAMMERER, Équation de la chaleur et mesures semi-classiques, Thèse, Univ. Paris XI, 1994. 
16. [16] P. GÉRARD, Mesures semi-classiques et ondes de Bloch (Séminaire EDPX 1990-1991, (16)). Zbl0739.35096
17. [17] P. GÉRARD and E. LEICHTNAM, Ergodic Properties of Eigenfunctions for the Dirichlet Problem (Duke Math. J., Vol. 71 (2), 1993, pp. 559-607). Zbl0788.35103MR94i:35146
18. [18] B. HELFFER, A. MARTINEZ and D. ROBERT, Ergodicité et limite semi-classique (Commun. in Math. Phys., Vol. 109, 1987, pp. 313-326). Zbl0624.58039MR88e:81029
19. [19] B. HELFFER and J. SJÖSTRAND, Équation de Harper (Lect. Notes in Physics, Vol. 345, 1989, pp. 118-197). Zbl0699.35189
20. [20] L. HÖRMANDER, The Analysis of Linear Partial Differential Operators, volume 3, Springer Verlag, 1985. Zbl0601.35001
21. [21] H. ISOZAKI and H. KITADA, A Remark on the Microlocal Resolvent Estimates for Two-Body Schrödinger Operators (RIMS Kyoto University, 1985). Zbl0611.35090
22. [22] H. ISOZAKI and H. KITADA, Scattering Matrices for Two-Body Schrödinger Operators (Sci. Papers College Arts Sci. Univ. Tokyo, Vol. 35, 1985, pp. 81-107). Zbl0615.35065MR87k:35196
23. [23] P. L. LIONS and T. PAUL, Sur les mesures de Wigner (Rev. Mat. Iberoamericana, Vol. 9 (3), 1993, pp. 553-618). Zbl0801.35117MR95a:58124
24. [24] A. MESSIAH, Mécanique Quantique, Dunod, 1965. 
25. [25] F. NIER, Schrödinger-Poisson Systems in dimension d ≤ 3 : the whole space case (Proc. Roy. Soc. Edin., Vol. 123 A, 1993, pp. 1179-1201). Zbl0807.35119MR94m:35217
26. [26] F. NIER, Asymptotic Analysis of a Scaled Wigner Equation (Transp. Theory Stat. Phys., Vol. 24 (4-5), 1995, pp. 591-628). Zbl0870.45003MR96c:82039
27. [27] M. REED and B. SIMON, Methods of Modern Mathematical Physics, Acad. Press, 1975. 
28. [28] D. ROBERT, Autour de l'approximation semi-classique, volume 68 of Progress in Mathematics, Birkhaüser, 1987. Zbl0621.35001MR89g:81016
29. [29] W. THIRRING, Quantum Mechanics of Atoms and Molecules, volume 3 of A Course in Mathematical Physics, Springer-Verlag, 1979. Zbl0462.46046
30. [30] X. P. WANG, Time-Delay Operators in the Semi-classical Limit. II. Short-range Potentials (Trans. Am. Math. Soc., Vol. 322(1), 1990, pp. 395-415). Zbl0714.35064
31. [31] K. YOSIDA, Functional Analysis, volume 123 of Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Springer-Verlag, 1968. Zbl0217.16001MR39 #741

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