The Complex WKB Method for Nonlinear Equations I

Linear Theory

Victor P. Maslov (Autor)

Buch | Softcover

VII, 304 Seiten

2012 | 1. Softcover reprint of the original 1st ed. 1994
Springer Basel (Verlag)
978-3-0348-9669-6 (ISBN)

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When this book was first published (in Russian), it proved to become the fountainhead of a major stream of important papers in mathematics, physics and even chemistry; indeed, it formed the basis of new methodology and opened new directions for research. The present English edition includes new examples of applications to physics, hitherto unpublished or available only in Russian. Its central mathematical idea is to use topological methods to analyze isotropic invariant manifolds in order to obtain asymptotic series of eigenvalues and eigenvectors for the multi-dimensional Schrödinger equation, and also to take into account the so-called tunnel effects. Finite-dimensional linear theory is reviewed in detail. Infinite-dimensional linear theory and its applications to quantum statistics and quantum field theory, as well as the nonlinear theory (involving instantons), will be considered in a second volume.

I. Equations and problems of narrow beam mechanics.- II. Hamiltonian formalism of narrow beams.- III. Approximate solutions of the nonstationary transport equation.- IV. Stationary Hamilton-Jacobi and transport equations.- V. Complex Hamiltonian formalism of compact (cyclic) beams.- VI. Canonical operators on Lagrangian manifolds with complex germ and their applications to spectral problems of quantum mechanics.- References.- Appendix A Complex germ generated by a linear connection.- Appendix B Asymptotic solutions with pure imaginary phase and the tunnel equation.- Appendix C Analytic asymptotics of oscillatory decreasing type (heuristic considerations).

Erscheint lt. Verlag	6.10.2012
Reihe/Serie	Progress in Mathematical Physics
Übersetzer	M.A. Shishkova, A.B. Sossinsky
Zusatzinfo	VII, 304 p.
Verlagsort	Basel
Sprache	englisch
Maße	155 x 235 mm
Gewicht	486 g
Themenwelt	Sachbuch/Ratgeber ► Natur / Technik ► Garten
	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Analysis • eigenvalue • Eigenvector • Field Theory • instanton • Jacobi • manifold • Mathematica • Mechanics • quantum field • quantum field theory • quantum mechanics • Schrödinger equation • Statistics
ISBN-10	3-0348-9669-7 / 3034896697
ISBN-13	978-3-0348-9669-6 / 9783034896696
Zustand	Neuware