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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... discussed. GTPack can be applied in a similar manner to both fields. The book itself is structured as follows. After a short introduction, the basic aspects of group theory are discussed in Part One. Part Two covers the application of ...
... discussed. GTPack can be applied in a similar manner to both fields. The book itself is structured as follows. After a short introduction, the basic aspects of group theory are discussed in Part One. Part Two covers the application of ...
Sida
... discussed to demonstrate that GTPack will be helpful also for problems other than electronic structure and photonics. GTPack has a long history in terms of its development. In this context, we would like to thank Diemo Ködderitzsch ...
... discussed to demonstrate that GTPack will be helpful also for problems other than electronic structure and photonics. GTPack has a long history in terms of its development. In this context, we would like to thank Diemo Ködderitzsch ...
Sida
... discussed the application of group theory in a series of papers between 1926 and 1928 [11] (see also H. WEYL 1928 [12]). Symmetry accounts for the degeneracy of energy levels of a quantum system. In a central field, for example, an ...
... discussed the application of group theory in a series of papers between 1926 and 1928 [11] (see also H. WEYL 1928 [12]). Symmetry accounts for the degeneracy of energy levels of a quantum system. In a central field, for example, an ...
Sida
... discussed (Figure 1.3). The square is located in the xy-plane. In general, the whole xy-plane could be covered completely by squares leading to a periodic arrangement like that of the STM image from the two MgO layers on Ag(001) in ...
... discussed (Figure 1.3). The square is located in the xy-plane. In general, the whole xy-plane could be covered completely by squares leading to a periodic arrangement like that of the STM image from the two MgO layers on Ag(001) in ...
Sida
... discussed. In general, symmetry operations can be distinguished in rotations and translations. Furthermore, rotations can be subdivided into proper and improper rotations depending on the sign of the determinant of the rotation matrix ...
... discussed. In general, symmetry operations can be distinguished in rotations and translations. Furthermore, rotations can be subdivided into proper and improper rotations depending on the sign of the determinant of the rotation matrix ...
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