The three dimensional time dependent generalized Dirac oscillator (Adiabatic solution) / Aitou ,Madjda  

Public ISBD Titre : The three dimensional time dependent generalized Dirac oscillator (Adiabatic solution) Type de document : texte imprimé Auteurs : Aitou ,Madjda, Auteur ; N. Chaabi, Directeur de thèse Editeur : Setif:UFA Année de publication : 2019 Importance : 1 vol (59 f .) Format : 29 cm Langues : Français (fre) Catégories : Thèses & Mémoires:Physique Mots-clés : Mecanique quantiquerelativiste Index. décimale : 530 Physique Résumé : L'oscillateur deDiracestl'undesdeveloppements les plusimportantsdanssaconstructionetses applications. C'estunegeneralisationdel'oscillateur harmonique danslecasrelativiste. Dans cetravail,nousconsideronsletheoreme adiabatique pourl'oscillateurdeDiracgeneraliseatrois dimensions avecparametresdependantdutemps.Nous determinonslasolutiondel'equationdeSchrodinger correspondantedanslescadredel'approximation adiabatique ,dontnouscalculonslaphasegeometrique correspondante(phasedeBerry Note de contenu : Sommaire Introduction 3 1 Chapter1:Relativisticquantummechanics5 1.1 Introduction...................................................5 1.2 Fourvectorformalism.............................................5 1.3 TheKleinGordenequation..........................................6 1.4 TheDiracequation...............................................7 1.4.1 RepresentationoftheDiracmatrices.................................8 1.4.2 ProbabilitydensityfortheDiracequation.............................9 1.4.3 Extremenon-relativisticlimitoftheDiracequation........................9 1.4.4 SpinoftheDiracparticles.......................................10 1.4.5 PlanewavesolutionsoftheDiracequation.............................11 1.5 Anti-particles|Holetheory.........................................14 2 Chapter2:ThetimedependentSchrodingerequation'sresolution16 2.1 Theexactmethods...............................................16 2.1.1 Evolutionoperator...........................................16 2.1.2 Changeofrepresentation.......................................16 2.1.3 Unitarytransformation........................................16 2.1.4 Invarianttheory............................................17 2.2 Approximationmethods............................................19 2.2.1 Perturbationtheory..........................................19 2.2.2 Thevariationalmethods........................................19 2.2.3 Suddenapproximation.........................................19 2.2.4 Adiabaticapproximation.......................................20 3 Chapter3:TheadiabaticapproximationandtheBerryphase22 3.1 Theadiabaticapproximation.........................................22 3.1.1 Theadiabaticapproximationinquantummechanics........................22 3.1.2 Theadiabatictheoreminthecaseofthediscretespectrum....................22 3.1.3 Thestatementoftheadiabatictheorem...............................23 3.2 TheBerryphase................................................24 3.2.1 Introduction..............................................24 3.2.2 SimplisticdenitionoftheBerryphase...............................25 3.2.3 GeneralformalismoftheBerryphase................................25 3.2.4 PhysicalinterpretationoftheBerryphase..............................26 3.2.5 Example:Berryphaseforanelectroninaslowlyvaryingmagneticeld.............28 3.3 TheBerryphaseapplications.........................................28 3.4 Berryphaseincondensedmatter:(Selectedexamples)...........................28 3.4.1 Berryphaseinblochbands......................................28 3.4.2 Thequantumhalleect(QHE)....................................30 4 Chapter4:Thethreedimensionalharmonicoscillator32 4.1 Introduction..................................................32 4.2 Threedimensionsharmonicoscillator....................................32 4.2.1 Operationaltreatmentofthreedimensionsquantumharmonicoscillator............32 4.2.2 Wavefunctionofthreedimensionsquantumharmonicoscillator..................34 4.2.3 Remarksontheoscillator.......................................34 5 Chapter5:ThethreedimensionaltimedependentgeneralizedDiracoscillator(Adiabatic solution) 36 5.1 Introduction..................................................36 5.2 ThethreedimensionaltimedependentgeneralizedDiracoscillator....................36 5.2.1 Introducetheproblem........................................36 5.2.2 Decouplingofspinors.........................................36 5.2.3 Thetotalkineticmomentum.....................................38 5.2.4 Separationofvariables.........................................38 5.2.5 Unitarytransformation........................................39 5.2.6 Solutionoftheequations.......................................39 Page1 TABLEOFCONTENTS 5.2.7 Timedependentsolution.......................................42 5.2.8 Calculationof Ijl and Njl . ......................................44 5.2.9 TheexplicitformfortheBerryphase................................45 Conclusion 46 Bibliographic references 47 Page2 Côte titre : MAPH/0334 En ligne : https://drive.google.com/file/d/1KI7CL_R31ReYwKcoBOGHXQq_Hm7xRil7/view?usp=shari [...] Format de la ressource électronique : pdf The three dimensional time dependent generalized Dirac oscillator (Adiabatic solution) [texte imprimé] / Aitou ,Madjda, Auteur ; N. Chaabi, Directeur de thèse . - [S.l.] : Setif:UFA, 2019 . - 1 vol (59 f .) ; 29 cm. Langues : Français (fre) Catégories : Thèses & Mémoires:Physique Mots-clés : Mecanique quantiquerelativiste Index. décimale : 530 Physique Résumé : L'oscillateur deDiracestl'undesdeveloppements les plusimportantsdanssaconstructionetses applications. C'estunegeneralisationdel'oscillateur harmonique danslecasrelativiste. Dans cetravail,nousconsideronsletheoreme adiabatique pourl'oscillateurdeDiracgeneraliseatrois dimensions avecparametresdependantdutemps.Nous determinonslasolutiondel'equationdeSchrodinger correspondantedanslescadredel'approximation adiabatique ,dontnouscalculonslaphasegeometrique correspondante(phasedeBerry Note de contenu : Sommaire Introduction 3 1 Chapter1:Relativisticquantummechanics5 1.1 Introduction...................................................5 1.2 Fourvectorformalism.............................................5 1.3 TheKleinGordenequation..........................................6 1.4 TheDiracequation...............................................7 1.4.1 RepresentationoftheDiracmatrices.................................8 1.4.2 ProbabilitydensityfortheDiracequation.............................9 1.4.3 Extremenon-relativisticlimitoftheDiracequation........................9 1.4.4 SpinoftheDiracparticles.......................................10 1.4.5 PlanewavesolutionsoftheDiracequation.............................11 1.5 Anti-particles|Holetheory.........................................14 2 Chapter2:ThetimedependentSchrodingerequation'sresolution16 2.1 Theexactmethods...............................................16 2.1.1 Evolutionoperator...........................................16 2.1.2 Changeofrepresentation.......................................16 2.1.3 Unitarytransformation........................................16 2.1.4 Invarianttheory............................................17 2.2 Approximationmethods............................................19 2.2.1 Perturbationtheory..........................................19 2.2.2 Thevariationalmethods........................................19 2.2.3 Suddenapproximation.........................................19 2.2.4 Adiabaticapproximation.......................................20 3 Chapter3:TheadiabaticapproximationandtheBerryphase22 3.1 Theadiabaticapproximation.........................................22 3.1.1 Theadiabaticapproximationinquantummechanics........................22 3.1.2 Theadiabatictheoreminthecaseofthediscretespectrum....................22 3.1.3 Thestatementoftheadiabatictheorem...............................23 3.2 TheBerryphase................................................24 3.2.1 Introduction..............................................24 3.2.2 SimplisticdenitionoftheBerryphase...............................25 3.2.3 GeneralformalismoftheBerryphase................................25 3.2.4 PhysicalinterpretationoftheBerryphase..............................26 3.2.5 Example:Berryphaseforanelectroninaslowlyvaryingmagneticeld.............28 3.3 TheBerryphaseapplications.........................................28 3.4 Berryphaseincondensedmatter:(Selectedexamples)...........................28 3.4.1 Berryphaseinblochbands......................................28 3.4.2 Thequantumhalleect(QHE)....................................30 4 Chapter4:Thethreedimensionalharmonicoscillator32 4.1 Introduction..................................................32 4.2 Threedimensionsharmonicoscillator....................................32 4.2.1 Operationaltreatmentofthreedimensionsquantumharmonicoscillator............32 4.2.2 Wavefunctionofthreedimensionsquantumharmonicoscillator..................34 4.2.3 Remarksontheoscillator.......................................34 5 Chapter5:ThethreedimensionaltimedependentgeneralizedDiracoscillator(Adiabatic solution) 36 5.1 Introduction..................................................36 5.2 ThethreedimensionaltimedependentgeneralizedDiracoscillator....................36 5.2.1 Introducetheproblem........................................36 5.2.2 Decouplingofspinors.........................................36 5.2.3 Thetotalkineticmomentum.....................................38 5.2.4 Separationofvariables.........................................38 5.2.5 Unitarytransformation........................................39 5.2.6 Solutionoftheequations.......................................39 Page1 TABLEOFCONTENTS 5.2.7 Timedependentsolution.......................................42 5.2.8 Calculationof Ijl and Njl . ......................................44 5.2.9 TheexplicitformfortheBerryphase................................45 Conclusion 46 Bibliographic references 47 Page2 Côte titre : MAPH/0334 En ligne : https://drive.google.com/file/d/1KI7CL_R31ReYwKcoBOGHXQq_Hm7xRil7/view?usp=shari [...] Format de la ressource électronique : pdf

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