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Explore the fundamental connections between group theory and quantum mechanics through this comprehensive lecture series spanning nearly 10 hours. Master the basics of symmetries in quantum systems, beginning with Wigner's theorem and progressing through linear representations of groups. Delve into irreducible representations, character theory, and Schur's lemma while examining their practical consequences in quantum mechanical contexts. Study orthogonality relations for characters, analyze the regular representation, and investigate class functions to understand how they determine the number of irreducible representations. Gain essential mathematical tools for understanding how symmetries constrain and illuminate quantum mechanical systems through rigorous group-theoretic methods.
