Group theory in solid state physics and photonics

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This textbook explores group theory and its applications in solid state physics, introducing two innovative aspects. It emphasizes problem-solving and utilizes Mathematica tools for concept visualization, enhancing understanding. The content is organized into three parts. The first part covers the fundamentals of group theory, expanding beyond standard examples to illustrate a wide range of applications. Part II focuses on applications in condensed matter physics, particularly the electronic structure of materials, where the integration of Mathematica with traditional derivations facilitates quicker comprehension. The extensive discussion demonstrates that group theory principles can also extend to different fields. In Part III, the text shifts to photonic applications, particularly photonic crystals in two and three dimensions, while also addressing other issues within photonics. The authors provide a Mathematica package, GTPack, available for download, which enables analytic considerations, numerical calculations, and visualizations using the same software. Although the Mathematica tools are showcased through basic examples, they are adaptable for more complex challenges stemming from the reader's research endeavors.