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The Resource Spectral asymptotics in the semi-classical limit, Mouez Dimassi, Johannes Sjöstrand

Spectral asymptotics in the semi-classical limit, Mouez Dimassi, Johannes Sjöstrand

Label
Spectral asymptotics in the semi-classical limit
Title
Spectral asymptotics in the semi-classical limit
Statement of responsibility
Mouez Dimassi, Johannes Sjöstrand
Creator
Contributor
Subject
Genre
Language
eng
Summary
Semiclassical approximation addresses the important relationship between quantum and classical mechanics. There has been a very strong development in the mathematical theory, mainly thanks to methods of microlocal analysis. This book develops the basic methods, including the WKB-method, stationary phase and h-pseudodifferential operators. The applications include results on the tunnel effect, the asymptotics of eigenvalues in relation to classical trajectories and normal forms, plus slow perturbations of periodic Schrödinger operators appearing in solid state physics. No previous specialized knowledge in quantum mechanics or microlocal analysis is assumed, and only general facts about spectral theory in Hilbert space, distributions, Fourier transforms and some differential geometry belong to the prerequisites. This book is addressed to researchers and graduate students in mathematical analysis, as well as physicists who are interested in rigorous results. A fairly large fraction can be (and has been) covered in a one semester course
Member of
Cataloging source
N$T
http://library.link/vocab/creatorName
Dimassi, Mouez
Dewey number
530.15/57222
Index
index present
LC call number
QC20.7.M53
LC item number
D56 1999eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Sjöstrand, J.
Series statement
London Mathematical Society lecture note series
Series volume
268
http://library.link/vocab/subjectName
  • Microlocal analysis
  • Quantum theory
  • Approximation theory
  • Spectral theory (Mathematics)
  • Mathematical physics
  • SCIENCE
  • Approximation theory
  • Mathematical physics
  • Microlocal analysis
  • Quantum theory
  • Spectral theory (Mathematics)
  • Quasiklassische Näherung
  • Analyse (wiskunde)
  • Operadores microlocais
  • Approximation, Théorie de l'
  • Théorie quantique
  • Physique mathématique
  • Théorie spectrale (Mathématiques)
  • Valeurs propres
  • Mécanique
Label
Spectral asymptotics in the semi-classical limit, Mouez Dimassi, Johannes Sjöstrand
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 209-220) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Trace class operators and applications of the functional calculus
  • More precise spectral asymptotics for non-critical Hamiltonians
  • Improvement when the periodic trajectories form a set of measure 0
  • A more general study of the trace
  • Spectral theory for perturbed periodic problems
  • Normal forms for some scalar pseudodifferential operators
  • Spectrum of operators with periodic bicharacteristics
  • Local symplectic geometry
  • The WKB-method
  • The WKB-method for a potential minimum
  • Self-adjoint operators
  • The method of stationary phase
  • Tunnel effect and interaction matrix
  • @h-pseudodifferential operators
  • Functional calculus for pseudodifferential operators
Control code
836871651
Dimensions
unknown
Extent
1 online resource (xi, 227 pages)
File format
unknown
Form of item
online
Isbn
9781107362796
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)836871651
Label
Spectral asymptotics in the semi-classical limit, Mouez Dimassi, Johannes Sjöstrand
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 209-220) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Trace class operators and applications of the functional calculus
  • More precise spectral asymptotics for non-critical Hamiltonians
  • Improvement when the periodic trajectories form a set of measure 0
  • A more general study of the trace
  • Spectral theory for perturbed periodic problems
  • Normal forms for some scalar pseudodifferential operators
  • Spectrum of operators with periodic bicharacteristics
  • Local symplectic geometry
  • The WKB-method
  • The WKB-method for a potential minimum
  • Self-adjoint operators
  • The method of stationary phase
  • Tunnel effect and interaction matrix
  • @h-pseudodifferential operators
  • Functional calculus for pseudodifferential operators
Control code
836871651
Dimensions
unknown
Extent
1 online resource (xi, 227 pages)
File format
unknown
Form of item
online
Isbn
9781107362796
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)836871651

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