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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... point groups at Γ and X are Oh and D4h, respectively. Table 9.2 Information from the character tables of C4v and Oh to evaluate 9.10. Characteristic elements of the classes are: . 12 Three-Dimensional Photonic Crystals Table 12.1 ...
... point groups at Γ and X are Oh and D4h, respectively. Table 9.2 Information from the character tables of C4v and Oh to evaluate 9.10. Characteristic elements of the classes are: . 12 Three-Dimensional Photonic Crystals Table 12.1 ...
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... group conditions are checked manually.1) Figure 3.2 Multiplication table of the non-Abelian point group C4v calculated using GTMultTable. Figure 3.3 Calculating the generators of the group C4v using GTGenerators. The group was installed ...
... group conditions are checked manually.1) Figure 3.2 Multiplication table of the non-Abelian point group C4v calculated using GTMultTable. Figure 3.3 Calculating the generators of the group C4v using GTGenerators. The group was installed ...
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... point group Td, illustrated using GTShowSymmetryElements. Figure 4.5 ... group. (a) The one-atomic square lattice is an example for a symmorphic space group. (b) ... C4v using GTInvSubGroups. Figure 4.14 Coloring schemes corresponding to ...
... point group Td, illustrated using GTShowSymmetryElements. Figure 4.5 ... group. (a) The one-atomic square lattice is an example for a symmorphic space group. (b) ... C4v using GTInvSubGroups. Figure 4.14 Coloring schemes corresponding to ...
Sida
... symmetry properties of C60. 5 Representation Theory Figure 5.1 Installation of the regular representation of the point group C4v using GTRegular-Representation. Figure 5.2 Installation of irreducible representations of the point group O ...
... symmetry properties of C60. 5 Representation Theory Figure 5.1 Installation of the regular representation of the point group C4v using GTRegular-Representation. Figure 5.2 Installation of irreducible representations of the point group O ...
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... symmetry classification given in Figure 11.12. Figure 11.14 Basis functions of the irreducible representations of C4v in terms of external plane waves. Figure 11.15 Calculating the compatibility relation between C4v and Cs ⊂ C4v using ...
... symmetry classification given in Figure 11.12. Figure 11.14 Basis functions of the irreducible representations of C4v in terms of external plane waves. Figure 11.15 Calculating the compatibility relation between C4v and Cs ⊂ C4v using ...
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