Advanced Quantum Mechanics

Materials and Photons

  • Rainer Dick

Part of the Graduate Texts in Physics book series (GTP)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Rainer Dick
    Pages 1-24
  3. Rainer Dick
    Pages 37-61
  4. Rainer Dick
    Pages 85-101
  5. Rainer Dick
    Pages 103-120
  6. Rainer Dick
    Pages 121-156
  7. Rainer Dick
    Pages 185-205
  8. Rainer Dick
    Pages 207-225
  9. Rainer Dick
    Pages 227-239
  10. Rainer Dick
    Pages 283-300
  11. Rainer Dick
    Pages 301-319
  12. Rainer Dick
    Pages 321-332
  13. Rainer Dick
    Pages 333-382
  14. Rainer Dick
    Pages 383-429
  15. Rainer Dick
    Pages 431-475

About this book

Introduction

In this updated and expanded second edition of a well-received and invaluable textbook, Prof. Dick 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. Advanced Quantum Mechanics, Materials and Photons 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.

This second edition includes an additional 62 new problems as well as expanded sections on relativistic quantum fields and applications of quantum 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 tr

ansition 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 for Eigen functions of one-dimensional Sturm-Liouville problems, logarithms of matrices, and Green’s functions in different dimensions.

Keywords

quantum aspects of materials BCH formula Lagrangian Field Theory Mehler’s formula Noether theorem Sturm-Liouville eigenfunctions capture cross sections degenerate perturbation theory Klein-Nishina cross section of Compton scattering Möller electron-electron scattering Bloch’s theorem Wannier states QED via quantization of classical fields

Authors and affiliations

  • Rainer Dick
    • 1
  1. 1.Dept of Physics & Engineering PhysicsUniversity of SaskatchewanSaskatoonCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-25675-7
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-25674-0
  • Online ISBN 978-3-319-25675-7
  • Series Print ISSN 1868-4513
  • Series Online ISSN 1868-4521
  • About this book