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Wir sind gerne für Sie daThis book deals with asymptotic solutions of linear and nonlinear equa tions which decay as h ---+ 0 outside a neighborhood of certain points, curves and surfaces. Such solutions are almost everywhere well approximated by the functions cp(x) exp{iS(x)/h}, x E 1R3, where S(x) is complex, and ImS(x) ~ o. When the phase S(x) is real (ImS(x) = 0), the method for obtaining asymp totics of this type is known in quantum mechanics as the WKB-method. We preserve this terminology in the case ImS(x) ~ 0 and develop the method for a wide class of problems in mathematical physics. Asymptotics of this type were constructed recently for many linear prob lems of mathematical physics; certain specific formulas were obtained by differ ent methods (V. M. Babich [5 -7], V. P. Lazutkin [76], A. A. Sokolov, 1. M. Ter nov [113], J. Schwinger [107, 108], E. J. Heller [53], G. A. Hagedorn [50, 51], V. N. Bayer, V. M. Katkov [21], N. A. Chernikov [35] and others). However, a general (Hamiltonian) formalism for obtaining asymptotics of this type is clearly required; this state of affairs is expressed both in recent mathematical and physical literature. For example, the editors of the collected volume [106] write in its preface: "One can hope that in the near future a computational pro cedure for fields with complex phase, similar to the usual one for fields with real phase, will be developed.
Produkteigenschaften
- Artikelnummer: 9783034896696
- Medium: Buch
- ISBN: 978-3-0348-9669-6
- Verlag: Birkhäuser
- Erscheinungstermin: 06.10.2012
- Sprache(n): Englisch
- Auflage: Erscheinungsjahr 2012
- Serie: Progress in Mathematical Physics
- Produktform: Kartoniert
- Gewicht: 482 g
- Seiten: 304
- Format (B x H x T): 155 x 235 x 18 mm
- Ausgabetyp: Kein, Unbekannt
Themen
- Naturwissenschaften
- Physik
- Physik Allgemein
- Theoretische Physik, Mathematische Physik, Computerphysik
- Mathematik | Informatik
- Mathematik
- Numerik und Wissenschaftliches Rechnen
- Angewandte Mathematik, Mathematische Modelle