The Resource Spectral asymptotics in the semi-classical limit, Mouez Dimassi, Johannes Sjöstrand
Spectral asymptotics in the semi-classical limit, Mouez Dimassi, Johannes Sjöstrand
Resource Information
The item Spectral asymptotics in the semi-classical limit, Mouez Dimassi, Johannes Sjöstrand represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri-St. Louis Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Spectral asymptotics in the semi-classical limit, Mouez Dimassi, Johannes Sjöstrand represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri-St. Louis Libraries.
This item is available to borrow from 1 library branch.
- 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
- Language
- eng
- Extent
- 1 online resource (xi, 227 pages)
- 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
- Isbn
- 9781107362796
- Label
- Spectral asymptotics in the semi-classical limit
- Title
- Spectral asymptotics in the semi-classical limit
- Statement of responsibility
- Mouez Dimassi, Johannes Sjöstrand
- Subject
-
- Approximation theory
- Approximation theory
- Approximation, Théorie de l'
- Electronic books
- Mathematical physics
- Mathematical physics
- Microlocal analysis
- Microlocal analysis
- Mécanique
- Operadores microlocais
- Physique mathématique -- Théorie asymptotique
- Quantum theory
- Quantum theory
- Quasiklassische Näherung
- SCIENCE -- Physics | Mathematical & Computational
- Spectral theory (Mathematics)
- Spectral theory (Mathematics)
- Théorie quantique
- Théorie spectrale (Mathématiques)
- Valeurs propres
- Analyse (wiskunde)
- 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
- 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
- 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
- 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
Subject
- Approximation theory
- Approximation theory
- Approximation, Théorie de l'
- Electronic books
- Mathematical physics
- Mathematical physics
- Microlocal analysis
- Microlocal analysis
- Mécanique
- Operadores microlocais
- Physique mathématique -- Théorie asymptotique
- Quantum theory
- Quantum theory
- Quasiklassische Näherung
- SCIENCE -- Physics | Mathematical & Computational
- Spectral theory (Mathematics)
- Spectral theory (Mathematics)
- Théorie quantique
- Théorie spectrale (Mathématiques)
- Valeurs propres
- Analyse (wiskunde)
Genre
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.umsl.edu/portal/Spectral-asymptotics-in-the-semi-classical-limit/052_SKjytsk/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.umsl.edu/portal/Spectral-asymptotics-in-the-semi-classical-limit/052_SKjytsk/">Spectral asymptotics in the semi-classical limit, Mouez Dimassi, Johannes Sjöstrand</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.umsl.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.umsl.edu/">University of Missouri-St. Louis Libraries</a></span></span></span></span></div>
