Advanced Quantum Mechanics

1. Front Matter

   Pages i-xix

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2. The Need for Quantum Mechanics

   • Rainer Dick

   Pages 1-23

3. Self-adjoint Operators and Eigenfunction Expansions

   • Rainer Dick

   Pages 25-34

4. Simple Model Systems

   • Rainer Dick

   Pages 35-55

5. Notions from Linear Algebra and Bra-Ket Notation

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   Pages 57-74

6. Formal Developments

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   Pages 75-89

7. Harmonic Oscillators and Coherent States

   • Rainer Dick

   Pages 91-105

8. Central Forces in Quantum Mechanics

   • Rainer Dick

   Pages 107-138

9. Spin and Addition of Angular Momentum Type Operators

   • Rainer Dick

   Pages 139-150

10. Stationary Perturbations in Quantum Mechanics

    • Rainer Dick

    Pages 151-162

11. Quantum Aspects of Materials I

    • Rainer Dick

    Pages 163-181

12. Scattering Off Potentials

    • Rainer Dick

    Pages 183-198

13. The Density of States

    • Rainer Dick

    Pages 199-208

14. Time-dependent Perturbations in Quantum Mechanics

    • Rainer Dick

    Pages 209-240

15. Path Integrals in Quantum Mechanics

    • Rainer Dick

    Pages 241-254

16. Coupling to Electromagnetic Fields

    • Rainer Dick

    Pages 255-271

17. Principles of Lagrangian Field Theory

    • Rainer Dick

    Pages 273-281

18. Non-relativistic Quantum Field Theory

    • Rainer Dick

    Pages 283-320

19. Quantization of the Maxwell Field: Photons

    • Rainer Dick

    Pages 321-353

20. Quantum Aspects of Materials II

    • Rainer Dick

    Pages 355-396

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.

• BCH formula
• Lagrangian Field Theory
• Mehler’s formula
• Noether theorem
• Sturm-Liouville eigenfunctions
• capture cross sections
• completeness of Sturm-Liouville eigenfunctions
• degenerate perturbation theory
• graduate textbook in quantum physics
• logarithms of matrices
• quantum aspects of materials
• quantum mechanics

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)

• University of Saskatchewan, Saskatoon, Canada

  Rainer Dick

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