LEADER 03757nam 22006975 450 001 996466657603316 005 20210913135930.0 010 $a3-540-45171-4 024 7 $a10.1007/b13355 035 $a(CKB)1000000000233139 035 $a(SSID)ssj0000320817 035 $a(PQKBManifestationID)11937805 035 $a(PQKBTitleCode)TC0000320817 035 $a(PQKBWorkID)10258154 035 $a(PQKB)10911289 035 $a(DE-He213)978-3-540-45171-6 035 $a(MiAaPQ)EBC5585122 035 $a(Au-PeEL)EBL5585122 035 $a(OCoLC)53925499 035 $a(PPN)23805490X 035 $a(EXLCZ)991000000000233139 100 $a20121227d2003 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aAdiabatic Perturbation Theory in Quantum Dynamics$b[electronic resource] /$fby Stefan Teufel 205 $a1st ed. 2003. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2003. 215 $a1 online resource (VI, 242 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1821 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-40723-5 327 $aIntroduction -- First-order adiabatic theory -- Space-adiabatic perturbation theory -- Applications and extensions -- Quantum dynamics in periodic media -- Adiabatic decoupling without spectral gap -- Pseudodifferential operators -- Operator-valued Weyl calculus for tau-equivariant symbols -- Related approaches -- List of symbols -- References -- Index. 330 $aSeparation of scales plays a fundamental role in the understanding of the dynamical behaviour of complex systems in physics and other natural sciences. A prominent example is the Born-Oppenheimer approximation in molecular dynamics. This book focuses on a recent approach to adiabatic perturbation theory, which emphasizes the role of effective equations of motion and the separation of the adiabatic limit from the semiclassical limit. A detailed introduction gives an overview of the subject and makes the later chapters accessible also to readers less familiar with the material. Although the general mathematical theory based on pseudodifferential calculus is presented in detail, there is an emphasis on concrete and relevant examples from physics. Applications range from molecular dynamics to the dynamics of electrons in a crystal and from the quantum mechanics of partially confined systems to Dirac particles and nonrelativistic QED. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1821 606 $aMathematical physics 606 $aOperator theory 606 $aPartial differential equations 606 $aTheoretical, Mathematical and Computational Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19005 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aMathematical physics. 615 0$aOperator theory. 615 0$aPartial differential equations. 615 14$aTheoretical, Mathematical and Computational Physics. 615 24$aOperator Theory. 615 24$aPartial Differential Equations. 676 $a530.12 676 $a510 s 686 $a81Q15$2msc 686 $a47G30$2msc 700 $aTeufel$b Stefan$4aut$4http://id.loc.gov/vocabulary/relators/aut$0149973 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466657603316 996 $aAdiabatic perturbation theory in quantum dynamics$9168813 997 $aUNISA LEADER 05636nam 2200757 450 001 9910555092603321 005 20221021141047.0 010 $a9781119513469 010 $a1-119-51346-4 010 $a1-118-55179-6 024 7 $a10.1002/9781119513469 035 $a(CKB)2670000000269723 035 $a(EBL)1051443 035 $a(OCoLC)823236113 035 $a(SSID)ssj0000754603 035 $a(PQKBManifestationID)12278998 035 $a(PQKBTitleCode)TC0000754603 035 $a(PQKBWorkID)10716544 035 $a(PQKB)10871782 035 $a(MiAaPQ)EBC1051443 035 $a(PPN)263076598 035 $a(EXLCZ)992670000000269723 100 $a20110322h20112011 uy| 0 101 0 $aeng 135 $aurbn#|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aApplied longitudinal analysis /$fGarrett M. Fitzmaurice, Nan M. Laird, James H. Ware 205 $a2nd ed. 210 1$aHoboken, New Jersey :$cWiley,$d[2011] 210 4$dİ2011 215 $a1 online resource (1309 p.) 225 1 $aWiley series in probability and statistics 300 $aDescription based upon print version of record. 311 08$a0-470-38027-6 320 $aIncludes bibliographical references (pages 671-693) and index. 327 $aCover; Half Title page; Title page; Copyright page; Dedication; Preface; Preface to First Edition; Acknowledgments; Part I: Introduction to Longitudinal and Clustered Data; Chapter 1: Longitudinal and Clustered Data; 1.1 Introduction; 1.2 Longitudinal and Clustered Data; 1.3 Examples; 1.4 Regression Models for Correlated Responses; 1.5 Organization of the Book; 1.6 Further Reading; Chapter 2: Longitudinal Data: Basic Concepts; 2.1 Introduction; 2.2 Objectives of Longitudinal Analysis; 2.3 Defining Features of Longitudinal Data; 2.4 Example: Treatment of Lead-Exposed Children Trial 327 $a2.5 Sources of Correlation in Longitudinal Data2.6 Further Reading; Part II: Linear Models for Longitudinal Continuous Data; Chapter 3: Overview of Linear Models for Longitudinal Data; 3.1 Introduction; 3.2 Notation and Distributional Assumptions; 3.3 Simple Descriptive Methods of Analysis; 3.4 Modeling the Mean; 3.5 Modeling the Covariance; 3.6 Historical Approaches; 3.7 Further Reading; Chapter 4: Estimation and Statistical Inference; 4.1 Introduction; 4.2 Estimation: Maximum Likelihood; 4.3 Missing Data Issues; 4.4 Statistical Inference; 4.5 Restricted Maximum Likelihood (REML) Estimation 327 $a4.6 Further ReadingChapter 5: Modeling the Mean: Analyzing Response Profiles; 5.1 Introduction; 5.2 Hypotheses Concerning Response Profiles; 5.3 General Linear Model Formulation; 5.4 Case Study; 5.5 One-Degree-of-Freedom Tests for Group by Time Interaction; 5.6 Adjustment for Baseline Response; 5.7 Alternative Methods of Adjusting for Baseline Response; 5.8 Strengths and Weaknesses of Analyzing Response Profiles; 5.9 Computing: Analyzing Response Profiles Using PROC MIXED in SAS; 5.10 Further Reading; Chapter 6: Modeling the Mean: Parametric Curves; 6.1 Introduction 327 $a6.2 Polynomial Trends in Time6.3 Linear Splines; 6.4 General Linear Model Formulation; 6.5 Case Studies; 6.6 Computing: Fitting Parametric Curves Using PROC MIXED in SAS; 6.7 Further Reading; Chapter 7: Modeling the Covariance; 7.1 Introduction; 7.2 Implications of Correlation among Longitudinal Data; 7.3 Unstructured Covariance; 7.4 Covariance Pattern Models; 7.5 Choice among Covariance Pattern Models; 7.6 Case Study; 7.7 Discussion: Strengths and Weaknesses of Covariance Pattern Models; 7.8 Computing: Fitting Covariance Pattern Models Using PROC MIXED in SAS; 7.9 Further Reading 327 $aChapter 8: Linear Mixed Effects Models8.1 Introduction; 8.2 Linear Mixed Effects Models; 8.3 Random Effects Covariance Structure; 8.4 Two-Stage Random Effects Formulation; 8.5 Choice among Random Effects Covariance Models; 8.6 Prediction of Random Effects; 8.7 Prediction and Shrinkage; 8.8 Case Studies; 8.9 Computing: Fitting Linear Mixed Effects Models Using PROC MIXED in SAS; 8.10 Further Reading; Chapter 9: Fixed Effects versus Random Effects Models; 9.1 Introduction; 9.2 Linear Fixed Effects Models; 9.3 Fixed Effects versus Random Effects: Bias-Variance Trade-off 327 $a9.4 Resolving the Dilemma of Choosing Between Fixed and Random Effects Models 330 $a"Since the publication of the first edition, the authors have solicited feedback from both the instructors who use the book as a text for their courses as well as the researchers who use the book as a resource for their research. 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