Spectral Asymptotics in the Semi-Classical Limit PDF Download
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Author: Mouez Dimassi
Publisher: Cambridge University Press
ISBN: 0521665442
Category : Mathematics
Languages : en
Pages : 243
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Book Description
This book presents the basic methods and applications in semiclassical approximation in the light of developments.
Author: Mouez Dimassi
Publisher: Cambridge University Press
ISBN: 0521665442
Category : Mathematics
Languages : en
Pages : 243
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Book Description
This book presents the basic methods and applications in semiclassical approximation in the light of developments.
Author: Mouez Dimassi
Publisher:
ISBN: 9781107362796
Category : SCIENCE
Languages : en
Pages : 241
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Book Description
This book presents the basic methods and applications in semiclassical approximation in the light of developments.
Author: Maciej Zworski
Publisher: American Mathematical Soc.
ISBN: 0821883208
Category : Mathematics
Languages : en
Pages : 448
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Book Description
"...A graduate level text introducing readers to semiclassical and microlocal methods in PDE." -- from xi.
Author: André Bach
Publisher: Springer Science & Business Media
ISBN: 1475744951
Category : Mathematics
Languages : en
Pages : 193
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Book Description
This book presents the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics in a pedagogical, way and is mainly addressed to non-specialists in the subject. It is based on lectures taught by the author over several years, and includes many exercises providing outlines of useful applications of the semi-classical theory.
Author: Huzihiro Araki
Publisher: World Scientific
ISBN: 9812387978
Category : Science
Languages : en
Pages : 288
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Book Description
This invaluable book presents reviews of some recent topics in the theory of Schrdinger operators. It includes a short introduction to the subject, a survey of the theory of the Schrdinger equation when the potential depends on the time periodically, an introduction to the so-called FBI transformation (also known as coherent state expansion) with application to the semi-classical limit of the S-matrix, an overview of inverse spectral and scattering problems, and a study of the ground state of the Pauli-Fierz model with the use of the functional integral. The material is accessible to graduate students and non-expert researchers.
Author: Victor Guillemin
Publisher:
ISBN: 9781571462763
Category : Fourier integral operators
Languages : en
Pages : 446
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Book Description
Author: Nicolas Lerner
Publisher: Springer Science & Business Media
ISBN: 3764385103
Category : Mathematics
Languages : en
Pages : 408
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Book Description
This book is devoted to the study of pseudo-di?erential operators, with special emphasis on non-selfadjoint operators, a priori estimates and localization in the phase space. We have tried here to expose the most recent developments of the theory with its applications to local solvability and semi-classical estimates for non-selfadjoint operators. The?rstchapter,Basic Notions of Phase Space Analysis,isintroductoryand gives a presentation of very classical classes of pseudo-di?erential operators, along with some basic properties. As an illustration of the power of these methods, we give a proof of propagation of singularities for real-principal type operators (using aprioriestimates,andnotFourierintegraloperators),andweintroducethereader to local solvability problems. That chapter should be useful for a reader, say at the graduate level in analysis, eager to learn some basics on pseudo-di?erential operators. The second chapter, Metrics on the Phase Space begins with a review of symplectic algebra, Wigner functions, quantization formulas, metaplectic group and is intended to set the basic study of the phase space. We move forward to the more general setting of metrics on the phase space, following essentially the basic assumptions of L. H ̈ ormander (Chapter 18 in the book [73]) on this topic.
Author: Philippe Blanchard
Publisher: Springer Science & Business Media
ISBN: 0817682023
Category : Science
Languages : en
Pages : 223
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Book Description
This volume explores multiscale methods as applied to various areas of physics and to the relative developments in mathematics. In the last few years, multiscale methods have lead to spectacular progress in our understanding of complex physical systems and have stimulated the development of very refined mathematical techniques. At the same time on the experimental side, equally spectacular progress has been made in developing experimental machinery and techniques to test the foundations of quantum mechanics.
Author: Dmitry E. Pelinovsky
Publisher: Cambridge University Press
ISBN: 1139503693
Category : Mathematics
Languages : en
Pages : 409
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Book Description
This comprehensive book describes modern methods in the analysis of reduced models of Bose–Einstein condensation in periodic lattices. Aimed at researchers and graduate students working in applied mathematics and physical sciences where nonlinear waves arise, its unique focus is on localized nonlinear waves in periodic potentials and lattices.
Author: Yaiza Canzani
Publisher: Springer Nature
ISBN: 3031315863
Category : Science
Languages : en
Pages : 123
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Book Description
This book discusses the modern theory of Laplace eigenfunctions through the lens of a new tool called geodesic beams. The authors provide a brief introduction to the theory of Laplace eigenfunctions followed by an accessible treatment of geodesic beams and their applications to sup norm estimates, L^p estimates, averages, and Weyl laws. Geodesic beams have proven to be a valuable tool in the study of Laplace eigenfunctions, but their treatment is currently spread through a variety of rather technical papers. The authors present a treatment of these tools that is accessible to a wider audience of mathematicians. Readers will gain an introduction to geodesic beams and the modern theory of Laplace eigenfunctions, which will enable them to understand the cutting edge aspects of this theory.
