Lectures related to Spectral Decomposition of Bounded Self-Adjoint Operators

Linear Operators: Basis Transformation and Eigenvalues

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Quantum Mechanics: Postulates and Observables

Explains the postulates of quantum mechanics and the representation of observables by operators.

Theory of Bounded Operators on Hilbert Space

Explores the theory of bounded operators on Hilbert space, including adjoint properties and self-adjointness.

Eigenvalue problem: Eigenbasis, Spectral theorem

Explores eigenvalue problems, eigenbasis, spectral theorem, and properties of normal operators.

Functional Analysis I: Spectral Theorem

Covers the spectral theorem, orthanormal sequences, and bounded linear operators in Hilbert spaces.

Postulates of Quantum Mechanics

Explains the postulates of Quantum Mechanics, focusing on self-adjoint operators and mathematical notation.

Essential Adjoints: Spectral Decomposition and Symmetric Operators

Explores spectral decomposition, essential self-adjointness, and symmetric operators in Hilbert spaces.

Postulates of Quantum Mechanics

Explores the postulates of Quantum Mechanics, emphasizing the state of a system as a complex-valued vector in a Hilbert space.

Linear Algebra: Vector Spaces & Operators

Explores vector spaces, linear transformations, matrices, eigenvalues, inner products, and operators.

Matrix Representation of Operators and Basis Transformation

Explores the matrix representation of operators and basis transformation in linear algebra.

Spectral Theorem for Operators

Explores the spectral theorem for operators in a Hilbert space.

Spectral Decomposition of Unbounded Operators

Explores the spectral decomposition of non-bounded operators and presents the spectral theorem for self-adjoint non-bounded operators.

Crash Course on Quantum Mechanics

Covers fundamental concepts in quantum mechanics, including vector spaces, superposition, observables, and inner product.

Functional Calculus: Operator Definition and Properties

Explores the definition and properties of the functional calculus for self-adjoint and bounded operators.

Quantum Mechanics: Measurement

Covers the axioms of quantum mechanics and the measurement of quantities in a quantum system.

Dynamical Approaches to Spectral Theory of Operators

Explores dynamical approaches to the spectral theory of operators, focusing on self-adjoint operators and Schrödinger operators with dynamically defined potentials.

Linear Maps and the Duality Principle in Mathematics

Covers the duality principle in linear algebra and its implications in mathematics.

Weak Formulation of Elliptic PDEs

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

Linear Algebra: Quantum Mechanics

Explores the application of linear algebra in Quantum Mechanics, emphasizing its importance in understanding materials properties.

Bounded Operators: Theory and Applications

Covers bounded operators between normed vector spaces, emphasizing the importance of continuity and exploring applications like the Fourier transform.