Group Theory in Solid State Physics and Photonics: Problem Solving with MathematicaJohn Wiley & Sons, 29 maj 2018 - 377 sidor 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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... Two-Dimensional Photonic Crystals 11.1 Photonic Band Structure and Symmetrized Plane Waves 11.2 Group Theoretical Classification of Photonic Band Structures 11.3 Supercells and Symmetry of Defect Modes 11.4 Uncoupled Bands 12 Three ...
... Two-Dimensional Photonic Crystals 11.1 Photonic Band Structure and Symmetrized Plane Waves 11.2 Group Theoretical Classification of Photonic Band Structures 11.3 Supercells and Symmetry of Defect Modes 11.4 Uncoupled Bands 12 Three ...
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... D: Technical Remarks on GTPack D.1 Structure of GTPack D.2 Installation of GTPack References Index End User License ... two mutually complex conjugate eigenvectors, while set B contains real eigenvectors only (complex conjugation ist ...
... D: Technical Remarks on GTPack D.1 Structure of GTPack D.2 Installation of GTPack References Index End User License ... two mutually complex conjugate eigenvectors, while set B contains real eigenvectors only (complex conjugation ist ...
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... two monolayers of MgO on Ag(001) (from [17], Figure 1) (With permission ... (d) reveals a waveguide structure prepared by a missing row of pores. (from ... 2 Symmetry Operations and Transformations of Fields Figure 2.1 Illustration of ...
... two monolayers of MgO on Ag(001) (from [17], Figure 1) (With permission ... (d) reveals a waveguide structure prepared by a missing row of pores. (from ... 2 Symmetry Operations and Transformations of Fields Figure 2.1 Illustration of ...
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... 2-dimensional (3- dimensional) lattice, go to the middle of each connecting line and construct an orthogonal line (plane). Take all crossing points of two lines (three planes) and form the convex hull. Figure 4.11 Reading the ...
... 2-dimensional (3- dimensional) lattice, go to the middle of each connecting line and construct an orthogonal line (plane). Take all crossing points of two lines (three planes) and form the convex hull. Figure 4.11 Reading the ...
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... (d) three unit cells of a (5,0) zigzag nanotube. Figure 4.20 Implementation ... two irreducible representations of the point group O using ... 2. Figure 5.11 Application of.
... (d) three unit cells of a (5,0) zigzag nanotube. Figure 4.20 Implementation ... two irreducible representations of the point group O using ... 2. Figure 5.11 Application of.
Innehåll
Basics Abstract Group Theory | |
Discrete Symmetry Groups in SolidState Physics and Photonics | |
Representation Theory | |
Symmetry and Representation Theory in kSpace | |
Solution of Maxwells Equations | |
TwoDimensional Photonic Crystals | |
ThreeDimensional Photonic Crystals | |
End User License Agreement | |
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Group Theory in Solid State Physics and Photonics: Problem Solving with ... Wolfram Hergert,R. Matthias Geilhufe Begränsad förhandsgranskning - 2018 |
Group Theory in Solid State Physics and Photonics: Problem Solving with ... Wolfram Hergert,R. Matthias Geilhufe Begränsad förhandsgranskning - 2018 |
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applied atoms band structure basis functions BRILLOUIN zone character projection operator character table classes CLEBSCH–GORDAN coefficients constructed coordinate corresponding cosets crystal field database decomposition Definition degeneracy denotes density dielectric direct product representation discussed double group eigenmodes eigenvalue electronic structure energy example given graphene group theory Hamiltonian improper rotations Installation invariant subgroup inversion irreducible representations lattice vectors linear magnetic master equation Mathematica matrix elements matrix representation modes molecule multiplication nanotubes nonsymmorphic notation parameters PAULI PAULI equation permittivity photonic band photonic band structure photonic crystal Physical Review plane waves point group C4v potential properties pseudopotential quaternion real-space representation matrices respect right cosets rotation axis rotation matrix SCHRÖDINGER equation Section shown in Figure SHUBNIKOV simple cubic space group spherical harmonics spin spin–orbit coupling splitting square lattice symmetry analysis symmetry elements symmetry group symmorphic space groups tight-binding Hamiltonian translation two-dimensional unit cell verified wave functions wave vector