Time-delay operators in semiclassical limit, finite range potentials
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 15 (1988) no. 1, pp. 1-34. 
@article{ASNSP_1988_4_15_1_1_0,
     author = {Wang, Xue Ping},
     title = {Time-delay operators in semiclassical limit, finite range potentials},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {1--34},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 15},
     number = {1},
     year = {1988},
     mrnumber = {1001028},
     zbl = {0706.35110},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1988_4_15_1_1_0/}
}
TY  - JOUR
AU  - Wang, Xue Ping
TI  - Time-delay operators in semiclassical limit, finite range potentials
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1988
SP  - 1
EP  - 34
VL  - 15
IS  - 1
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_1988_4_15_1_1_0/
LA  - en
ID  - ASNSP_1988_4_15_1_1_0
ER  - 
%0 Journal Article
%A Wang, Xue Ping
%T Time-delay operators in semiclassical limit, finite range potentials
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1988
%P 1-34
%V 15
%N 1
%I Scuola normale superiore
%U http://www.numdam.org/item/ASNSP_1988_4_15_1_1_0/
%G en
%F ASNSP_1988_4_15_1_1_0
Wang, Xue Ping. Time-delay operators in semiclassical limit, finite range potentials. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 15 (1988) no. 1, pp. 1-34. http://www.numdam.org/item/ASNSP_1988_4_15_1_1_0/

[1] S. Agmon, "Spectral properties of Schrödinger operators and scattering theory". Ann. Scuola Norm. Sup. Pisa (4), 2 (1975), 151-218. | EuDML | Numdam | MR | Zbl

[2] S. Albeverio - T. Arede, "The relation between quantum mechanics and classical mechanics, A survey of some mathematical aspects". To appear in Proc. Como Conf. 1983, Plenum.

[3] J. Chazarain, "Sur le comportement semi-classique du spectre et de l'amplitude de diffusion d' un Hamiltonien". In "Singularities in Boundary Value Problems", pp. 1-17, ed. H. Garnir, R. Reidel, Publ. 1981. | Zbl

[4] V. Enss - B. Simon, "Finite total cross sections in non-relativistic quantum mechanics". Comm. Math. Phys. 76 (1980), 177-209. | MR | Zbl

[5] R. Froese - I. Herbst, "Exponential bounds and absence of positive eigenvalue for N-body Schrödinger operators". Comm. Math., Phys. (1982). | MR | Zbl

[6] D. Fujiwara, "A construction of fundamental solution for the Schrödinger equation". J. Anal. Math., 35 (1979), 41-96. | MR | Zbl

[7] V. Guillemin, "Sojourn times and asymptotic properties of scattering matrix". Publ. RIMS, Kyoto Univ. Suppl. 12, (1977), 69-88. | MR | Zbl

[8] K. Gustafon - K. Sinha, "On the Eisenbud-Wigner formula for time delay". Lett., in Math. Phys., 4 (1980), 381. | MR | Zbl

[9] B. Helffer - D. Robert, "Comportement semi-classique des Hamiltoniens quantiques elliptiques". Ann. Inst. Fourier (Grenoble), 31 (3) (1983), 169-223. | EuDML | Numdam | MR | Zbl

[10] B. Helffer - D. Robert, "Calcul fonctionnel par la transformation de Mellin et opérateurs admissibles". J. Funct. Anal., 53 (3) (1983), 246-268. | MR | Zbl

[11] K. Hepp, "The classical limit for quantum mechanical correlation functions". Comm. Math. Phys., 35 (1974), 265-277. | MR

[12] L. Hormander, "The Weyl calculus of pseudo-differential operators". Comm. Pure Appl. Math., 32 (1979), 359-443. | MR | Zbl

[13] W. Hunziker, "The S-matrix in classical mechanics". Comm. Math. Phys., 8 (1968), 75-104. | MR | Zbl

[14] A. Jensen, "Time-delay in potential scattering theory, some "geometric" results". Comm. Math. Phys., 82 (1981), 435-456. | MR | Zbl

[15] A. Jensen, "On Lavine's formula for time-delay". Math. Scand., 54 (1984), 253-261. | EuDML | MR | Zbl

[16] R. Lavine, "Commutators and local decay, in "scattering theory in mathematical physics". pp. 141-156, eds. J.A. Lavita and J.P. Marchand, D. Reidel Publ. 1974. | Zbl

[17] P. Lax - R. Phillips, "The time-delay operator and a related trace formula". Topics in functional analysis, pp. 197-215, eds. I. Gohberg, M. Kac; Acad. Press, 1978. | MR | Zbl

[18] Ph. Martin, "Time delay of quantum scattering processes". Acta Phys. Austriaca, Suppl. 23 (1981), 157-208. | MR

[19] V.P. Maslov - M.V. Fedoriuk, "Semi-classical approximation in Quantum mechanics", D. Reidel, Dordrecht, 1981. | Zbl

[20] E. Mourre, "Link between the geometrical and the spectral transformation approches in scattering theory". Comm. Math. Phys. 68 (1979), 91-94. | MR | Zbl

[21] E. Mourre, "Opérateurs conjugués et propriétés de propagation". Comm. Math. Phys., 91 (1983), 279-300. | MR | Zbl

[22] H. Narnhofer, "Another definition for time-delay". Phys. Rev., D 22 (1980), 2387-2390. | MR

[23] H. Narnhofer, "Time-delay and dilation properties in scattering theory". J. Math. Phys., 25 (1984), 987-991. | MR | Zbl

[24] V. Petkov - G. Popov, "Asymptotic behaviour of scattering phase for non-trapping obstacles". Ann. Inst. Fourier Grenoble, 32 (1982), 111-149. | EuDML | Numdam | MR | Zbl

[25] Yu. N. Protas, "Quasiclassical asymptotics of the scattering amplitude for the scattering of a plane wave by inhomogeneities of the medium". Mth. USSR Sb., 45 (1983), 487-506. | Zbl

[26] M. Reed - B. Simon, "Methods of modern mathematical physics, III, scattering theory". Acad. Press. New-York, 1979. | MR | Zbl

[27] M. Reed - B. Simon, "Method of modern mathematical physics, IV analysis of operators". Acad. Press, New-York, 1978. | MR | Zbl

[28] D. Robert, "Autour de l'approximation semi-classique". Notas de Curso, n° 21, Recife, 1983.

[29] D. Robert, "Calcul fonctionnel sur les opérateurs admissibles et applications". J. Funct. Anal., 45 (1), (1982), 74-94. | MR | Zbl

[30] D. Robert - H. Tamura, "Semi-classical bounds for resolvents of Schrödinger operators and asymptotic for scattering phase". Comm. P.D.E., 9 (10) (1984), 1017-1058. | MR | Zbl

[31] D. Robert - H. Tamura, "Semi-classical asymptotic for spectral function of Schrödinger operators and applications to scattering problems", to appear.

[32] B. Simon, "Wave operators for classical particle scattering". Comm. Math. Phys., 23 (1971), 37-48. | MR | Zbl

[33] B. Simon, "The classical limit of quantum partition functions". Comm. Math. Phys., 71 (1980), 247-276. | MR | Zbl

[34] M. Siruge - A. Siruge-Collin - A. Truman, "Semi-classical approximation and microcanonical ensemble". Annales de l'IHP, 41 (4) (1984), 429-444. | EuDML | Numdam | MR | Zbl

[35] B.R. Vainberg, "Quasi-classical approximation in stationary scattering problems". Funct. Anal. Appl. (Engl. Transl.), 11 (1977), 6-18. | Zbl

[36] X.P. Wang, "Comportement semi-classique de traces partielles" . C.R. Acad. Sc. Paris, 299 (17) (1984), 867-870. | MR | Zbl

[37] X.P. Wang, "Asymptotic behaviour of spectral means of pseudo-differential operators". J. Approx. Theory and Appl., 1 (3), 1985. | MR | Zbl

[38] X.P. Wang, "Approximation semi-classique de l'Equation de Heisenberg, Comm. Math. Phys. 104 (1986). | MR | Zbl

[39] X.P. Wang, "Opérateurs de temps-retard dans la théorie de diffusion". Exposé aux Journées de St. Jean de Mont, Juin 1985. | Numdam

[40] K. Yajima, "The quasi-classical limit of quantum scattering theory". Comm. Math. Phys. 69 (1979), 101-129. | MR | Zbl

[41] K. Yajima, "The quasi-classical limit of scattering amplitude I, finite range potentials". Preprint. | Zbl

[42] X.P. Wang, "Time-decay of scattering solutions and smothness of resolvent for Schrödinger operators", J. Diff. Equations, 71 (1988), 348-396. | MR | Zbl

[43] X.P. Wang, "Opérateurs de temps-retard dans la théorie de la diffusion, C.R. Acad. Sc. Paris, 301 (17) (1985), 789-791. | MR | Zbl

[44] J.M. Bony - N. Lerner, "Quantification asymptotique et micro-localisation d' ordre supérieure". Séminaire Equations aux Dérivées Partielles 1986-1987, Ecole Polytechnique, Palaiseau. | EuDML | Numdam | MR | Zbl