Lectures related to Adjoint of Linear Operators on Inner Product Spaces

Linear Operators: Basis Transformation and Eigenvalues

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

Matrix Representation of Operators and Basis Transformation

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

Eigenvalue problem: Eigenbasis, Spectral theorem

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

Postulates of Quantum Mechanics

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

Linear Operators: Quantum Mechanics and Linear Algebra

Explores the role of linear operators in Quantum Mechanics and linear algebra, emphasizing eigenvalues and basis transformations.

Linear Algebra: Unitary Operators

Delves into unitary operators, self-adjoint properties, and spectral theorems in linear algebra.

Linear Algebra: Vector Spaces & Operators

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

Quantum Mechanics: Postulates and Observables

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

Functional Analysis I: Spectral Theorem

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

Theory of Bounded Operators on Hilbert Space

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

Functional Analysis I: Norms and Bounded Operators

Explores norms and bounded operators in functional analysis, demonstrating their properties and applications.

Spectral Decomposition of Unbounded Operators

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

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 Operators: Boundedness and Spaces

Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.

Linear Algebra: Quantum Mechanics

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

Extension of Linear Transformations

Covers the extension of bounded linear transformations and the free propagator in L^2 spaces.

Hermitian Operators and Spectral Theorem

Explores Hermitian operators, auto-adjoint properties, and spectral theorems in Hermitian spaces.

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.

Distributional Derivatives

Explores distributional derivatives, continuity, boundedness of linear operators, and weak-* continuity.

Measurement: Quantum State and Observables

Discusses measurement in Quantum Mechanics, focusing on state vectors, observables, eigenvalues, and probabilities.