Linear Operators: Quantum Mechanics and Linear Algebra

This lecture covers the motivation for studying linear operators in Quantum Mechanics (QM) and their essential role in representing measurable quantities. It delves into the properties of self-adjoint linear operators, eigenvalues, eigenvectors, and their significance in QM systems. The lecture also explores the importance of linear operators in solving linear ODEs and PDEs, emphasizing the spectral problem and eigenbasis identification. Concepts of linear algebra, such as adjoint operators and basis transformations, are discussed in the context of linear operators. The lecture concludes with the representation of vectors and operators in different bases, including orthonormal bases.