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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... Figure 2.6 The usage of GTQuaternionQ and GTQMultiplication in GTPack. Figure 2.7 The application of GTQInverse. Figure 2.8 The calculation of the conjugate quaternion, the absolute value of a quaternion, and the polar angle of a.
... Figure 2.6 The usage of GTQuaternionQ and GTQMultiplication in GTPack. Figure 2.7 The application of GTQInverse. Figure 2.8 The calculation of the conjugate quaternion, the absolute value of a quaternion, and the polar angle of a.
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Problem Solving with Mathematica Wolfram Hergert, R. Matthias Geilhufe. value of a quaternion, and the polar angle of ... quaternions, or symbols of symmetry elements with the help of GTGetSU2Matrix. The symbol C3z denotes a ...
Problem Solving with Mathematica Wolfram Hergert, R. Matthias Geilhufe. value of a quaternion, and the polar angle of ... quaternions, or symbols of symmetry elements with the help of GTGetSU2Matrix. The symbol C3z denotes a ...
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... quaternion GTQMultiplicationMultiplication of quaternions GTQInverse Gives the inverse of a quaternion GTQAbs Gives the absolute value of a quaternion GTQConjugate Gives the conjugate of a quaternion GTQPolar Gives the polar angle of a ...
... quaternion GTQMultiplicationMultiplication of quaternions GTQInverse Gives the inverse of a quaternion GTQAbs Gives the absolute value of a quaternion GTQConjugate Gives the conjugate of a quaternion GTQPolar Gives the polar angle of a ...
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... quaternions. Starting from symbols, matrices, or quaternions GTGetEulerAngles can be used to obtain an associated set of Euler angles. The application of the command is shown in Figure 2.5. 2.1.3 EULER–RODRIGUES Parameters and Quaternions ...
... quaternions. Starting from symbols, matrices, or quaternions GTGetEulerAngles can be used to obtain an associated set of Euler angles. The application of the command is shown in Figure 2.5. 2.1.3 EULER–RODRIGUES Parameters and Quaternions ...
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... the rotation can be written as (2.22) (2.23) This transformation is known as the conical transformation, where the vector r rotates on a cone around the vector n. Within GTPack rotations can be represented in terms of quaternions.
... the rotation can be written as (2.22) (2.23) This transformation is known as the conical transformation, where the vector r rotates on a cone around the vector n. Within GTPack rotations can be represented in terms of quaternions.
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