×

zbMATH — the first resource for mathematics

The quasi-classical limit of quantum scattering theory. (English) Zbl 0425.35076

MSC:
35P25 Scattering theory for PDEs
35B40 Asymptotic behavior of solutions to PDEs
35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
35Q99 Partial differential equations of mathematical physics and other areas of application
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Agmon, S.: Spectral Properties of Schrödinger operators and scattering theory. Ann. Scuola Nor. Pisa, Ser IV,2.2, 151-218 (1975) · Zbl 0315.47007
[2] Asada, K., Fujiwara, D.: On some oscillatory integral transformations in L2 (?n). Jpn. J. Math.4, 299-361 (1978) · Zbl 0402.44008
[3] Fujiwara, D.: A construction of the fundamental solution for Schrödinger equation. J. d’Analyse Math. (In press) · Zbl 0418.35032
[4] Hepp, K.: The classical limit for quantum mechanical correlation functions. Commun. Math. Phys.35, 265-277 (1974) · doi:10.1007/BF01646348
[5] Hepp, K.: On the classical limit in Quantum mechanics. Unpublished note, ETH-Zürich (1974)
[6] Herbst, W.: Classical scattering with long range forces. Commun. Math. Phys.35, 193-214 (1974) · Zbl 0309.70011 · doi:10.1007/BF01646193
[7] Hörmander, L.: Fourier integral operators. Acta. Math.127, 79-183 (1971) · Zbl 0212.46601 · doi:10.1007/BF02392052
[8] Hörmander, L.: The existence of wave operators in scattering theory. Math. Z.146, 69-91 (1976) · Zbl 0319.35059 · doi:10.1007/BF01213717
[9] Hunziker, W.: The S-matrix in classical mechanics. Commun. Math. Phys.,8, 283-299 (1968) · Zbl 0159.55001 · doi:10.1007/BF01646269
[10] Kuroda, S. T.: Scattering theory for differential operators. J. Math. Soc. Japan25, 75-104 (1973) · Zbl 0245.47006 · doi:10.2969/jmsj/02510075
[11] Maslov, V.P.: Théorie des perturbations et méthodes asymptotiques (Translation from Russian) Paris: Dunod 1972
[12] Simon, B.: Wave operators for classical particle scattering. Commun. Math. Phys.23, 37-48 (1971) · Zbl 0238.70012 · doi:10.1007/BF01877595
[13] Dollard, J. D.: Scattering into cones. I. Potential scattering. Commun. Math. Phys.12, 193-203 (1969) · doi:10.1007/BF01661573
[14] Yajima, K.: The quasi-classical limit of quantum scattering theory. II. Long range scattering. Preprint, University of Virginia (1978) · Zbl 0454.35069
[15] Landau, L. D., Lifschitz, E. M.: Course of theoretical physics, Vol. 1, Mechanics (Translation from Russian). New York: Pergamon Press 1969.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.