Rainer Dick

Advanced Quantum Mechanics (eBook, PDF)

Materials and Photons

• Format: PDF

Produktbeschreibung

Advanced Quantum Mechanics: Materials and Photons is a textbook which emphasizes the importance of advanced quantum mechanics for materials science and all experimental techniques which employ photon absorption, emission, or scattering. Important aspects of introductory quantum mechanics are covered in the first seven chapters to make the subject self-contained and accessible for a wide audience. The textbook can therefore be used for advanced undergraduate courses and introductory graduate courses which are targeted towards students with diverse academic backgrounds from the Natural Sciences or Engineering. To enhance this inclusive aspect of making the subject as accessible as possible, Appendices A and B also provide introductions to Lagrangian mechanics and the covariant formulation of electrodynamics. Other special features include an introduction to Lagrangian field theory and an integrated discussion of transition amplitudes with discrete or continuous initial or final states. Once students have acquired an understanding of basic quantum mechanics and classical field theory, canonical field quantization is easy. Furthermore, the integrated discussion of transition amplitudes naturally leads to the notions of transition probabilities, decay rates, absorption cross sections and scattering cross sections, which are important for all experimental techniques that use photon probes. Quantization is first discussed for the Schrödinger field before the relativistic Maxwell, Klein-Gordon and Dirac fields are quantized. Quantized Schrödinger field theory is not only important for condensed matter physics and materials science, but also provides the easiest avenue to general field quantization and is therefore also useful for students with an interest in nuclear and particle physics. The quantization of the Maxwell field is performed in Coulomb gauge. This is the appropriate and practically most useful quantization procedure in condensed matter physics, chemistry, and materials science because it naturally separates the effects of Coulomb interactions, exchange interactions, and photon scattering. The appendices contain additional material that is usually not found in standard quantum mechanics textbooks, including a completeness proof of eigenfunctions of one-dimensional Sturm-Liouville problems, logarithms of matrices, and Green's functions in different dimensions.

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Produktdetails

• Verlag: Springer-Verlag GmbH
• Seitenzahl: 552
• Erscheinungstermin: 11. Januar 2012
• Englisch
• ISBN-13: 9781441980779
• Artikelnr.: 37355290

Autorenporträt

Rainer Dick was educated in Stuttgart and Hamburg, and worked at the University of Munich and the Institute for Advanced Study in Princeton before accepting a faculty position at the University of Saskatchewan. He has served at the Canadian national level as Chair of the Division of Theoretical Physics of the Canadian Association of Physicists and on several national committees. He has also served as Secretary of the Commission for Mathematical Physics of the International Union of Pure and Applied Physics. Dick's research interests are influenced by the versatility of quantum theory and the ubiquity of quantum effects, and span a wide array of topics from materials research to astroparticle physics and brane cosmology.

Inhaltsangabe

Chapter1. The Need for Quantum Mechanics.- Chapter2. Self-adjoint Operators and Eigenfunction Expansions.- Chapter3. Simple Model Systems.- Chapter4. Notions from Linear Algebra and Bra-Ket Notation.- Chapter5. Formal Developments.- Chapter6. Harmonic Oscillators and Coherent States.- Chapter7. Central Forces in Quantum Mechanics.- Chapter8. Spin and Addition of Angular Momentum Type Operators.- Chapter9. Stationary Perturbations in Quantum Mechanics.- Chapter10. Quantum Aspects of Materials I.- Chapter11. Scattering Off Potentials.- Chapter12. The Density of States.- Chapter13. Time-dependent Perturbations in Quantum Mechanics.- Chapter14. Path Integrals in Quantum Mechanics.- Chapter15. Coupling to Electromagnetic Fields.- Chapter16. Principles of Lagrangian Field Theory.- Chapter17. Non-relativistic Quantum Field Theory.- Chapter18. Quantization of the Maxwell Field: Photons.- Chapter19. Epistemic and Ontic Quantum States.- Chapter20. Quantum Aspects of Materials II.- Chapter21.Dimensional Effects in Low-dimensional Systems.- Chapter22. Relativistic Quantum Fields.- Chapter23. Applications of spinor QED.

Rezensionen

From the reviews:

"Book goes through quantum mechanics starting from its foundations, that are introduced along the historical development. It also includes recent topics ... that is necessary to understand quantum effects inside chemistry, material science, microelectronics and photonics. The style is always very didactic, mathematical tools are introduced in a very gradual way ... . Some chapters may constitute an initial course in quantum mechanics, the others cover a graduate course in advanced quantum mechanics and can also provide a very useful introduction to quantum field theory." (Bassano Vacchini, Zentralblatt MATH, Vol. 1247, 2012)