Advanced Quantum Mechanics

This textbook introduces quantum mechanics from the discovery of photons all the way to field quantization, relativistic quantum fields, and photon-matter interactions. Contrary to the traditional textbook approach to quantum mechanics, which is strongly influenced by the joint historic development of quantum physics with atomic and nuclear physics, emphasis is placed on the important role of quantum theory for our modern understanding of materials and electromagnetic radiation. Quantum mechanics has become an indispensable tool for research in materials science, nanotechnology, and photonics. Energy levels and wave functions of atomic systems still hold important clues for the behavior of donor atoms in semiconductors or for energy levels in quantum dots, but quantum technologies are evolving so rapidly that the basic connections have to be made at an earlier stage. Furthermore, many experimental and diagnostic techniques in materials science and technology are based on photon probes, and therefore photon scattering is discussed along with emission and absorption processes.The book is written for a wide audience of students in physics, chemistry, and engineering, but does not compromise the mathematical rigor necessary for comprehension. Special appendices cover the completeness of Sturm-Liouville eigenfunctions, the Baker-Campbell-Hausdorff formula, Mehler s formula, and logarithms of matrices.The book can be used both for advanced undergraduate courses and graduate courses in quantum mechanics. It will be particularly welcomed by professors and researchers who want to prepare their students for experimental or theoretical work in materials science, condensed matter physics, or investigations which require photon-matter interactions in any way.