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Lecture notes in Atomic Physics

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Atomic physics and Quantum mechanics acompanying notes Univ.-Prof. Dr. Enrico Arrigoni TU Graz - Austria Version from: November 13, 2010 Students of the course 515.300 “Atomphysik und Quantenmechanik fu¨r ET/MB” can access a more complete version of the lecture notes (access password restricted) interested people can ask me by e-mail: arrigonitugraz.at PDF presentation using LaTeX and the Beamer Class http://latex-beamer.sourceforge.net Enrico Arrigoni (TU Graz) Atomic Physics and Quantum Mechanics WS 2009 1 / 193Content of this lecture Content of this lecture Mainly from S. M. Blinder “Introduction to Quantum Mechanics in Chemistry, Materials Science, and Biology” 1 Introduction: atoms and electromagnetic waves 2 Failures of classical physics Blackbody radiation Photoelectric effect Line spectra 3 Wave and Particle duality Double-slit experiment Light carries momentum: Compton scattering Matter (Electrons) as waves 4 Bohr’s atom Enrico Arrigoni (TU Graz) Atomic Physics and Quantum Mechanics WS 2009 2 / 193Content of this lecture Content of this lecture Mainly from S. M. Blinder “Introduction to Quantum Mechanics in Chemistry, Materials Science, and Biology” 1 Introduction: atoms and electromagnetic waves 2 Failures of classical physics Blackbody radiation Photoelectric effect Line spectra 3 Wave and Particle duality Double-slit experiment Light carries momentum: Compton scattering Matter (Electrons) as waves 4 Bohr’s atom Enrico Arrigoni (TU Graz) Atomic Physics and Quantum Mechanics WS 2009 2 / 193Content of this lecture Content of this lecture Mainly from S. M. Blinder “Introduction to Quantum Mechanics in Chemistry, Materials Science, and Biology” 1 Introduction: atoms and electromagnetic waves 2 Failures of classical physics Blackbody radiation Photoelectric effect Line spectra 3 Wave and Particle duality Double-slit experiment Light carries momentum: Compton scattering Matter (Electrons) as waves 4 Bohr’s atom Enrico Arrigoni (TU Graz) Atomic Physics and Quantum Mechanics WS 2009 2 / 193Content of this lecture Content of this lecture Mainly from S. M. Blinder “Introduction to Quantum Mechanics in Chemistry, Materials Science, and Biology” 1 Introduction: atoms and electromagnetic waves 2 Failures of classical physics Blackbody radiation Photoelectric effect Line spectra 3 Wave and Particle duality Double-slit experiment Light carries momentum: Compton scattering Matter (Electrons) as waves 4 Bohr’s atom Enrico Arrigoni (TU Graz) Atomic Physics and Quantum Mechanics WS 2009 2 / 193Content of this lecture Content of this lecture 5 The wave function and Schr¨odinger equation Euristic derivation of Schr¨odinger equation Time-independent Schr¨odinger equation Interpretation of the wave function Summary: Schr¨odinger equation 6 Quantum mechanics of some simple systems Free particle Particle in a box Generalisations of the particle in a box Tunnel effect Three-dimensional box 7 Principles and Postulates of Quantum mechanics Postulates of Quantum Mechanics Enrico Arrigoni (TU Graz) Atomic Physics and Quantum Mechanics WS 2009 3 / 193Content of this lecture Content of this lecture 5 The wave function and Schr¨odinger equation Euristic derivation of Schr¨odinger equation Time-independent Schr¨odinger equation Interpretation of the wave function Summary: Schr¨odinger equation 6 Quantum mechanics of some simple systems Free particle Particle in a box Generalisations of the particle in a box Tunnel effect Three-dimensional box 7 Principles and Postulates of Quantum mechanics Postulates of Quantum Mechanics Enrico Arrigoni (TU Graz) Atomic Physics and Quantum Mechanics WS 2009 3 / 193Content of this lecture Content of this lecture 5 The wave function and Schr¨odinger equation Euristic derivation of Schr¨odinger equation Time-independent Schr¨odinger equation Interpretation of the wave function Summary: Schr¨odinger equation 6 Quantum mechanics of some simple systems Free particle Particle in a box Generalisations of the particle in a box Tunnel effect Three-dimensional box 7 Principles and Postulates of Quantum mechanics Postulates of Quantum Mechanics Enrico Arrigoni (TU Graz) Atomic Physics and Quantum Mechanics WS 2009 3 / 193Content of this lecture Content of this lecture 8 Angular momentum and electron spin First step: “particle on a ring” Second step: “particle on the surface of a sphere” Electron spin 9 The Hydrogen atom Schr¨odinger equation and separation of variables Qualitative solution Classification of atomic orbitals 10 Many-electron atoms and the periodic table Pauli principle Building-up principle Hund’s rule Enrico Arrigoni (TU Graz) Atomic Physics and Quantum Mechanics WS 2009 4 / 193Content of this lecture Content of this lecture 8 Angular momentum and electron spin First step: “particle on a ring” Second step: “particle on the surface of a sphere” Electron spin 9 The Hydrogen atom Schr¨odinger equation and separation of variables Qualitative solution Classification of atomic orbitals 10 Many-electron atoms and the periodic table Pauli principle Building-up principle Hund’s rule Enrico Arrigoni (TU Graz) Atomic Physics and Quantum Mechanics WS 2009 4 / 193Content of this lecture Content of this lecture 8 Angular momentum and electron spin First step: “particle on a ring” Second step: “particle on the surface of a sphere” Electron spin 9 The Hydrogen atom Schr¨odinger equation and separation of variables Qualitative solution Classification of atomic orbitals 10 Many-electron atoms and the periodic table Pauli principle Building-up principle Hund’s rule Enrico Arrigoni (TU Graz) Atomic Physics and Quantum Mechanics WS 2009 4 / 193Suggested literature Suggested literature I 1 S. M. Blinder, Introduction to Quantum Mechanics in chemistry, Material Science, and Biology see also http://www.umich.edu/ chem461/ the class essentially based on this book 2 L. van Dommelen Fundamental Quantum Mechanics for Engineers notes available at http://www.eng.fsu.edu/ dommelen/quantum 3 J. E. House, Fundamentals of Quantum Chemistry some mathematical aspects are treated in more detail here 4 P. W. Atkins, Physical Chemistry Chap. 2 also a good book, many details and examples, many physical aspects discussed. 5 P. A. Tipler and R. A. Llewellyn, Moderne Physik simpler treatment Enrico Arrigoni (TU Graz) Atomic Physics and Quantum Mechanics WS 2009 5 / 193Suggested literature Suggested literature II 6 J.J. Sakurai, Modern Quantum Mechanics High level book 7 D. Ferry Quantum Mechanics: An Introduction for Device Physicists and Electrical Engineer More advanced, special topics of interest for material physicists. Device physics, transport theory. 8 Applets http://www.quantum-physics.polytechnique.fr/en/index.html Enrico Arrigoni (TU Graz) Atomic Physics and Quantum Mechanics WS 2009 6 / 193Introduction: atoms and electromagnetic waves 1 Introduction: atoms and electromagnetic waves 2 Failures of classical physics 3 Wave and Particle duality 4 Bohr’s atom 5 The wave function and Schr¨odinger equation 6 Quantum mechanics of some simple systems 7 Principles and Postulates of Quantum mechanics 8 Angular momentum and electron spin Enrico Arrigoni (TU Graz) Atomic Physics and Quantum Mechanics WS 2009 7 / 193 9 The Hydrogen atomIntroduction: atoms and electromagnetic waves (See also Blinder, Chap 1.1-1.2) Enrico Arrigoni (TU Graz) Atomic Physics and Quantum Mechanics WS 2009 8 / 193Introduction: atoms and electromagnetic waves Blinder,Chap. 1, Pages 1-5 Enrico Arrigoni (TU Graz) Atomic Physics and Quantum Mechanics WS 2009 8 / 193Failures of classical physics 1 Introduction: atoms and electromagnetic waves 2 Failures of classical physics Blackbody radiation Photoelectric effect Line spectra 3 Wave and Particle duality 4 Bohr’s atom 5 The wave function and Schr¨odinger equation 6 Quantum mechanics of some simple systems 7 Principles and Postulates of Quantum mechanics Enrico Arrigoni (TU Graz) Atomic Physics and Quantum Mechanics WS 2009 9 / 193Failures of classical physics Blackbody radiation (See also Blinder, Chap 1.3-1.6) Enrico Arrigoni (TU Graz) Atomic Physics and Quantum Mechanics WS 2009 9 / 193Failures of classical physics Blackbody radiation Blackbody radiation Enrico Arrigoni (TU Graz) Atomic Physics and Quantum Mechanics WS 2009 10 / 193Failures of classical physics Blackbody radiation Blinder,Chap. 1, Pages 6-7 Enrico Arrigoni (TU Graz) Atomic Physics and Quantum Mechanics WS 2009 10 / 193