Explore the mathematical foundations of quantum mechanics in this 26-minute video lecture on position and momentum operators. Delve into the complex mathematics underlying quantum theory, including linear algebra and differential equations. Learn about operators, their applications to wavefunctions, and the crucial roles of position and momentum operators in quantum mechanics. Discover how these concepts differ from classical physics and relate to key principles like the Heisenberg Uncertainty Principle and wave-particle duality. Gain insights into the de Broglie principle, properties of operators, and the commutator of position and momentum. While advanced mathematical knowledge is recommended, links to prerequisite math topics are provided for a comprehensive understanding of this fundamental aspect of modern physics.