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Quantique 2013 Chimie Atkins 17/07/13 16:28 Page1 PHYquanPER_quantique 2013_chimie_atkins 17/07/13 16:28 Page1 Pérez Carles Pujol I I Pérez Carles Pujol Pujol I I Quantique I fondements et applications Carles I Quantique Cet ouvrage, découpé en 20 leçons quasi En outre, sont examinés les progrès considérables autonomes, rassemble les fondements et apparus au cours des dernières décennies, tant sur le plan les applications de la quantique. fondamental, avec la levée des divers paradoxes, que sur le développement de l’optique quantique et des multi- ples applications en métrologie. L’ouvrage se termine Pérez fondements et applications Qu’est-ce que la quantique ? par une ouverture relativiste rendue nécessaire par les Dans la première leçon, on présente la quantique, en progrès qu’ont permis, sur le plan de la pensée et des soulignant les aspects historiques et épistémologiques applications, la théorie de Dirac et l’électrodynamique de cette discipline, et en rappelant ses nombreuses quantique. avec 250 exercices et problèmes résolus implications, non seulement en physique atomique et moléculaire, mais aussi en physique nucléaire, en chimie, De nombreux exemples, plus de 250 exercices en physique de la matière condensée et dans le domaine et problèmes résolus émergent des nanosciences. L’ouvrage s’adresse d’abord aux étudiants de licence (L2, L3) et de la première année du master (M1), mais sa Aspects fondamentaux et applications présentation didactique, avec ses nombreux exemples et Le fil conducteur de l’ouvrage peut être résumé par ses 250 exercices et problèmes résolus, ainsi que l’accent le slogan « un maximum de physique avec un minimum mis sur le développement historique et épistémologique, de formalisme ». Ainsi, en appliquant l’équation de devraient aussi intéresser les candidats aux concours Schrödinger à des systèmes unidimensionnels, sont rapide- de l’enseignement (CAPES, agrégations, etc.), et plus ment abordés les effets de confinement, de quantification, largement toutes les personnes concernées par la de tunnel et de diffusion. Dans ce contexte, l’évolution, le physique et son impact dans toutes les autres disciplines déterminisme, l’indiscernabilité, la superposition d’états et scientifiques, voire même en philosophie. l’intrication, qui sont analysés en détail dans la seconde moitié de l’ouvrage, sont très tôt considérés. Les auteurs José-Philippe Pérez, Professeur émérite de a Ouvrage construit en 20 leçons, progressives et quasi l’Université de Toulouse, UPS-IRAP. autonomes Robert Carles, Professeur à l'Université de Toulouse, a Fondements, ordres de grandeurs et applications concrètes UPS-CEMES. fondements et applications a Développement historique et épistémologique Olivier Pujol, Maître de conférences à l’Université a Aspect plus actuel : introduction à la théorie quantique de Lille, LOA. des champs a De nombreux exemples, 250 exercices et problèmes résolus a Annexes mathématiques et simulations numériques ISBN : 978-2-8041-0778-9 Quantique www.deboeck.com 9 782804 107789 PHYQUANPER Conception graphique : Primo&Primo® Primo&Primo® : graphique Conception D.R. © illu : Quantique fondements et applications PHYQUANPER-pgeTitre.indd 1 19/08/13 11:16 Des mêmes auteurs PÉREZ J.-Ph., PUJOL O., LAGOUTE Ch., PUECH P., ANTERRIEU É., Physique une introduction PÉREZ J.-Ph., LAGOUTE Ch., PUJOL O., DESMEULES É., Leçons de physique. Une approche moderne Chez le même éditeur ASLANGUL C., Mécanique quantique 1. Fondements et applications ASLANGUL C., Mécanique quantique 2. Développement et applications à basse énergie, 2e éd. ASLANGUL C., Mécanique quantique 3. Corrigés détaillés et commentés des exercices et problèmes FOX M., Optique quantique HECHT E., Physique HOBSON M., EFSTATHIOU G., LASENBy A., Relativité générale PHYQUANPER-pgeTitre.indd 2 19/08/13 11:16 Pérez | Carles | Pujol Quantique fondements et applications avec 250 exercices et problèmes résolus PHYQUANPER-pgeTitre.indd 3 19/08/13 11:16 Illustration de couverture L’image utilisée pour illustrer la couverture de l’ouvrage est celle d’un nanoSQUID donnée par un microscope à force atomique. Dans un tel dispositif en forme d’anneau, constitué d’un supraconducteur, d’un nanotube de carbone et d’un plot, on réalise des interférences quantiques avec des paires d’électrons ; plusieurs effets quantiques interviennent alors : l’effet tunnel, l’indiscernabilité des objets, la quantification du flux magnétique, la conductance d’un fil quantique et la discrétisation des niveaux d’énergie dans une boîte quantique. En raison de sa grande sensibilité, le nanoSQUID permet de détecter des moments magnétiques élémentaires. Cette image est issue de travaux menés, dans le cadre du laboratoire CEMES (Centre d’Élaboration de matériaux et d’Études Structurales) de Toulouse et des laboratoires CRTBT (Centre de Recherche sur les Très Basses Températures) et LLN (Laboratoire Louis Néel) de Grenoble, par J.-P. Cleuziou, W. Wernsdorfer, V. Bouchiat, T. Ondarçuhu et M. Monthioux (Nature Nanotechnology, vol. 1, 53-59, 2006). Pour toute information sur notre fonds et les nouveautés dans votre domaine de spécialisation, consultez notre site web: www.deboeck.com © De Boeck Supérieur s.a., 2013 Rue des Minimes, 39 B-1000 Bruxelles Pour la traduction et l’adaptation française Tous droits réservés pour tous pays. Il est interdit, sauf accord préalable et écrit de l’éditeur, de reproduire (notamment par photocopie) partiellement ou totalement le présent ouvrage, de le stocker dans une banque de données ou de le communiquer au public, sous quelque forme et de quelque manière que ce soit. Imprimé en Belgique Dépôt légal: Bibliothèque nationale, Paris: septembre 2013 Bibliothèque royale de Belgique, Bruxelles: 2013/0074/215 ISBN 978-2-8041-0778-9 PHYQUANPER-pgeTitre.indd 4 19/08/13 11:16 i i / / i “PHYQUANPER” — 2013 8 27 — 9:04 — page 5 — #1 i Table des matières Table des matières v Avant-Propos xi Notations et symboles xiv Constantes fondamentales . xiv Notations . xv Alphabet grec . xvii Multiples en notation scientifique . xvii Les grands noms de la physique xviii La quantique en vingt questions xl Leçons 1 1 Qu’est-ce que la quantique? 3 Les fondements de la physique classique . 4 La constante de Planck . 8 Les quatre interactions fondamentales . 16 Les concepts de la quantique . 19 Les fondements de la quantique . 22 Les applications de la quantique . 26 Les différentes synthèses en physique . 30 2 Le photon : première approche 37 Rappel sur les ondes électromagnétiques . 38 Rayonnement du corps noir . 44 Effet photoélectrique . 46 Effet Compton . 50 Autres interactions lumière-matière . 55 Détection et atténuation d’un rayonnement . 58 3 Quantification de l’énergie des atomes 69 Spectre de raies de l’atome d’hydrogène . 70 Interprétation historique de Bohr . 71 Atomes hydrogénoïdes et muoniques . 74 i i i i i i / / i “PHYQUANPER” — 2013 8 27 — 9:04 — page 6 — #2 i vi Table des matières Excitation des atomes . 77 Limites du modèle de Bohr . 83 4 Relation de de Broglie. Inégalités d’Heisenberg 91 Hypothèse fondamentale de Louis de Broglie . 91 Confirmations expérimentales . 96 Interprétation probabiliste . 103 Groupe d’ondes de probabilité . 107 Inégalités spatiales d’Heisenberg . 110 Effets de phase . 115 5 Équation de Schrödinger. États libres 127 Équation de Schrödinger non relativiste . 128 Courant de probabilité . 133 États stationnaires d’un objet physique . 135 États libres à une dimension . 137 Flux d’objets physiques libres . 140 Réflexion et transmission sur une marche . 143 Applications . 155 6 Effet tunnel et diffusion à une dimension 165 Mise en évidence expérimentale . 166 Transmission par effet tunnel . 168 Facteur de transmission en intensité . 171 Interprétation de divers phénomènes . 174 Applications de l’effet tunnel . 178 Diffusion à une dimension . 183 Analyse matricielle . 187 7 Confinement quantique à une dimension 195 Approches classique et quantique . 195 Puits rectangulaire infiniment profond . 197 Approximation classique . 202 Puits quantique de profondeur finie . 204 Exemples physiques de puits . 209 Mesures des grandeurs dans un état confiné . 212 Représentation en quantité de mouvement . 214 8 Oscillateur harmonique et excitations élémentaires 225 Oscillateur harmonique en physique classique . 225 Oscillateur harmonique en quantique . 227 Exemples et ordres de grandeur . 232 Spectrométries de vibration . 237 i i i i i i / / i “PHYQUANPER” — 2013 8 27 — 9:04 — page 7 — #3 i Table des matières vii 9 Systèmes à plusieurs dimensions 249 Systèmes à variables séparables . 250 Prise en compte des symétries . 251 Système 0 D et boîte quantique . 255 Système 1D et fil quantique . 258 Système 2 D et puits quantique . 265 Systèmes 3 D . 271 Réflexion et transmission . 277 10 Couplage de puits quantiques : de l’atome au solide 291 Couplage de deux oscillateurs mécaniques . 291 Couplage par effet tunnel de deux puits quantiques . 301 Comparaison des cas classique et quantique . 312 Autres exemples de couplage . 313 Chaîne périodique d’oscillateurs classiques . 316 Couplage tunnel d’une chaîne périodique de puits . ..
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