no. 1
Asymptotic completeness in long range scattering. II
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 18 (1985) no. 1, pp. 57-87. 
@article{ASENS_1985_4_18_1_57_0,
     author = {Muthuramalingam, Pl. and Sinha, Kalyan B.},
     title = {Asymptotic completeness in long range scattering. {II}},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {57--87},
     publisher = {Elsevier},
     volume = {Ser. 4, 18},
     number = {1},
     year = {1985},
     doi = {10.24033/asens.1484},
     mrnumber = {87a:35144},
     zbl = {0584.47009},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/asens.1484/}
}
TY  - JOUR
AU  - Muthuramalingam, Pl.
AU  - Sinha, Kalyan B.
TI  - Asymptotic completeness in long range scattering. II
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 1985
SP  - 57
EP  - 87
VL  - 18
IS  - 1
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.24033/asens.1484/
DO  - 10.24033/asens.1484
LA  - en
ID  - ASENS_1985_4_18_1_57_0
ER  - 
%0 Journal Article
%A Muthuramalingam, Pl.
%A Sinha, Kalyan B.
%T Asymptotic completeness in long range scattering. II
%J Annales scientifiques de l'École Normale Supérieure
%D 1985
%P 57-87
%V 18
%N 1
%I Elsevier
%U http://www.numdam.org/articles/10.24033/asens.1484/
%R 10.24033/asens.1484
%G en
%F ASENS_1985_4_18_1_57_0
Muthuramalingam, Pl.; Sinha, Kalyan B. Asymptotic completeness in long range scattering. II. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 18 (1985) no. 1, pp. 57-87. doi : 10.24033/asens.1484. http://www.numdam.org/articles/10.24033/asens.1484/

[1] W. O. Amrein, J. M. Jauch and K. B. Sinha, Scattering Theory in Quantum Mechanics, W. Benjamin, Reading, 1977. | MR | Zbl

[2] P. Alsholm, Wave Operators for Long Range Scattering (J. Math. Anal. Appl., Vol. 59, 1977, p. 550). | MR | Zbl

[3] L. Hörmander, The Existence of Wave Operators in Scattering Theory, (Math. Zeit., Vol. 146, 1976, pp. 69-91). | MR | Zbl

[4] A. M. Berthier and P. Collet, Wave Operators for Momentum Dependent long Range Potential (Ann. Inst. Henri-Poincaré, Section A, Vol. 27, 1977, pp. 279-293). | Numdam | MR | Zbl

[5] W. O. Amrein, Ph. A. Martin and B. Misra, On the Asymptotic Condition of Scattering Theory (Helv. Phys. Acta, Vol. 43, 1970, pp. 313-344). | MR | Zbl

[6] J. D. Dollard, Asymptotic Convergence and the Coulomb Interaction (J. Math. Phys., Vol. 5, 1964, pp. 729-738). | MR

[7] R. Lavine, Absolute Continuity of Positive Spectrum for Schrödinger Operators with Long Range Potentials (J. Func. Anal., Vol. 12, 1973, pp. 30-54). | MR | Zbl

[8] T. Ikebe, Spectral Representations for Schrödinger Operators with Long Range Potentials. Perturbation by short range potentials (Publ. Res. Inst. Math. Sc., Vol. 11, 1976, pp. 551-558). | MR | Zbl

[9] Y. Saito, Spectral Representations for Schrödinger Operators with long Range potential (Lecture Notes in Math. No. 727, Berlin. Heildelberg, New York, Springer-Verlag, 1979). | MR | Zbl

[10] J. Weidmann, Über Spectraltheorie von SturmLiouville-Operatoren (Math. Zeit., Vol. 98, 1967, pp. 268-302). | MR | Zbl

[11] V. Georgescu, Méthodes stationnaires pour des potentiels à longue portée à symétrie sphérique (Thèse, Université de Genève, 1974).

[12] T. Ikebe and H. Isozaki, A Stationary Approach to the Existence and Completeness of Long Range wave Operators, preprint, Kyoto Univ., 1980.

[13] H. Kitada, Scattering Theory for Schrodinger Operators with Long Range Potentials II (J. Math. Soc. Japan, Vol. 30, 1978, pp. 603-632). | MR | Zbl

[14] S. Agmon, Some new Results in Spectral and Scattering Theory of Differential Operators on L²(Rn) [Séminaire Goulaouic-Schwartz, 1978-1979, Centre de Mathématiques, Palaiseau (Lecture notes)]. | Numdam | Zbl

[15] L. E. Thomas, On the Algebraic Theory of Scattering (J. Func. Anal., Vol. 15, 1974, pp. 364-377). | MR | Zbl

[16] V. Enss, Asymptotic Completeness for Quantum Mechanical Potential Scattering II. Singular and Long Range Potentials (Ann. Phys. New York, Vol. 119, 1979, pp. 117-132). | MR | Zbl

[17] V. Enss, Geometric Methods in Spectral and Scattering Theory of Schrödinger Operators, Section 7 in (Rigorous Atomic and Molecular Physics), G. Velo and A. Weightman eds., New York, Plenum, 1981.

[18] P. A. Perry, Propagation of States in Dilation Analytic Potentials and Asymptotic Completeness (Comm. Math. Phys., Vol. 81, 1981, pp. 243-259). | MR | Zbl

[19] Pl. Muthuramalingam and K. B. Sinha, Asymptotic Evoluation of Certain Observables and Completeness in Coulomb Scattering I (J. Func. Analysis, Vol. 55, 1983). | Zbl

[20] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1966. | MR | Zbl

[21] M. Reed and B. Simon, Methods of Modern Mathematical Physics, II. Fourier Analysis, Self Adjointness, Academic Press, New York, 1972. | Zbl

[22] M. Reed and B. Simon, Methods of Modern Mathematical Physics, III. Scattering Theory, Academic Press, New York, 1979. | MR | Zbl

[23] M. Reed and B. Simon, Methods of Modern Mathematical Physics, IV. Analysis of Operators, Academic Press, New York, 1978. | MR | Zbl

[24] P. A. Perry, Mellin Transforms and Scattering Theory, I. Short Range Potentials (Duke Math. J., Vol. 47, 1980, pp. 187-193). | MR | Zbl

[25] E. B. Davies, Quantum Theory of Open Systems, Academic Press, New York, 1976. | MR | Zbl

[26] E. B. Davies, On Enss' Approach to Scattering Theory (Duke Math. J. Vol. 47, 1980, pp. 171-185). | MR | Zbl

[27] J. Ginibre, La Méthode "dépendant du temps" dans le problème de la complétude asymptotique, preprint, Université de Paris-Sud, LP THE 80/10, 1980.

[28] E. Mourre, Opérateurs conjugués et propriétés de propagation (Commun. Math. Phys., Vol. 91, 1983, pp. 279-300). | MR | Zbl

[29] A. Jensen, E. Mourre and P. Perry, Multiple Commutator Estimates and Resolvent Smoothness in Quantum Scattering Theory, Preprint, 1983, Caltech, CA 91125.

Cité par Sources :