In this episode of "Mathematical Foundations of Quantum Mechanics," Lecture 3, Part B, Dr. Hudis delves into the eigenfunctions of position and momentum in QM. He explores the three fundamental symmetry operators essential for the study of quantum mechanics: the position operator, the momentum operator, and the phase operator. These operators are key to manipulating quantum wavefunctions and are crucial for modeling atoms and subatomic particles. This lecture focuses on these vital mathematical operations, providing a solid foundation for understanding quantum mechanics.