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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... corresponding to BETHE, BOUCKAERT, SMOLUCHOWSKI and WIGNER (BSW), and MULLIKEN. The 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 ...
... corresponding to BETHE, BOUCKAERT, SMOLUCHOWSKI and WIGNER (BSW), and MULLIKEN. The 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 ...
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... corresponding to SHUBNIKOV groups of the third kind for a square. Figure 4.15 Installation of magnetic point groups in GTPack. Figure 4.16 Construction of magnetic lattices [61]. (a) Primitive lattice; (b) colored lattice; (c) magnetic ...
... corresponding to SHUBNIKOV groups of the third kind for a square. Figure 4.15 Installation of magnetic point groups in GTPack. Figure 4.16 Construction of magnetic lattices [61]. (a) Primitive lattice; (b) colored lattice; (c) magnetic ...
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... corresponding to the irreducible representations occurring in the decomposition given in (9.25). The classes are characterized by elements selected in Figure 9.5. Figure 9.7 Construction of symmetry-adapted linear combinations (SALC's) ...
... corresponding to the irreducible representations occurring in the decomposition given in (9.25). The classes are characterized by elements selected in Figure 9.5. Figure 9.7 Construction of symmetry-adapted linear combinations (SALC's) ...
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... corresponding k-space calculation (solid line). (a) Comparison of DOS (real-space cluster of 74 atoms); (b) comparison of DOS (real-space cluster of 2146 atoms). Figure 9.32 Weights of eigenstates for a real-space tight-binding ...
... corresponding k-space calculation (solid line). (a) Comparison of DOS (real-space cluster of 74 atoms); (b) comparison of DOS (real-space cluster of 2146 atoms). Figure 9.32 Weights of eigenstates for a real-space tight-binding ...
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... (corresponds to Nwaves). Figure 12.8 Symmetry-adapted vector spherical waves for point group Oh. ohctN is the character table of the point group, ohctM is the character table corrected to include the sign change for improper rotations ...
... (corresponds to Nwaves). Figure 12.8 Symmetry-adapted vector spherical waves for point group Oh. ohctN is the character table of the point group, ohctM is the character table corrected to include the sign change for improper rotations ...
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