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This lecture covers the fundamental principles of quantum mechanics, focusing on the Schrödinger equation, wave functions, and energy quantization for confined particles. It explores the concept of particle confinement in potential wells, the quantization of energy levels, and the solutions for particles in a box in one, two, and three dimensions. The lecture also delves into the calculation of energy levels, wave functions, and the implications of quantum mechanics in understanding the behavior of particles in confined spaces.