Group Theory in Solid State Physics and Photonics: Problem Solving with Mathematica
While group theory and its application to solid state physics is well established, this textbook raises two completely new aspects. First, it provides a better understanding by focusing on problem solving and making extensive use of Mathematica tools to visualize the concepts. Second, it offers a new tool for the photonics community by transferring the concepts of group theory and its application to photonic crystals.
Clearly divided into three parts, the first provides the basics of group theory. Even at this stage, the authors go beyond the widely used standard examples to show the broad field of applications. Part II is devoted to applications in condensed matter physics, i.e. the electronic structure of materials. Combining the application of the computer algebra system Mathematica with pen and paper derivations leads to a better and faster understanding. The exhaustive discussion shows that the basics of group theory can also be applied to a totally different field, as seen in Part III. Here, photonic applications are discussed in parallel to the electronic case, with the focus on photonic crystals in two and three dimensions, as well as being partially expanded to other problems in the field of photonics.
The authors have developed Mathematica package GTPack which is available for download from the book's homepage. Analytic considerations, numerical calculations and visualization are carried out using the same software. While the use of the Mathematica tools are demonstrated on elementary examples, they can equally be applied to more complicated tasks resulting from the reader's own research.
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Part One Basics of Group Theory
Part Two Applications in Electronic Structure Theory
Part Three Applications in Photonics
Part Four Other Applications
Appendix A Spherical Harmonics
Appendix B Remarks on Databases
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Group Theory in Solid State Physics and Photonics: Problem Solving with ...
Wolfram Hergert,Christian Matyssek,R. Matthias Geilhufe
Begränsad förhandsgranskning - 2018
angle applied atoms band structure basis functions Brillouin zone character table classes Clebsch–Gordan coefficients command constructed contains coordinate corresponding cosets crystal field cubic database decomposition Definition degeneracy denotes density dielectric direct product representation discussed double group eigenmodes eigenvalue energy example given group C4v group theory GTPack Hamiltonian improper rotations installed invariant subgroup inversion irreducible representations KGaA lattice vectors linear magnetic master equation Mathematica matrix elements matrix representation modes molecule nanotubes notation orthogonal parameters Pauli Pauli equation permittivity photonic band photonic band structure photonic crystal Physics and Photonics plane waves point group properties quaternion real-space representation matrices right cosets rotation axis rotation matrix Schrödinger equation Section shown in Figure Shubnikov space groups spherical harmonics spin spin–orbit coupling structure calculation symmetry elements symmetry group symmorphic space groups Theorem tight-binding Hamiltonian tion transformation translation two-dimensional unit cell verified