Lectures related to Linear Operators: Quantum Mechanics and Linear Algebra

Linear Operators: Basis Transformation and Eigenvalues

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

Postulates of Quantum Mechanics

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

Quantum Mechanics: Postulates and Observables

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

Matrix Representation of Operators and Basis Transformation

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

Linear Algebra: Quantum Mechanics

Explores the application of linear algebra in quantum mechanics, emphasizing vector spaces, Hilbert spaces, and the spectral theorem.

Eigenvalue problem: Eigenbasis, Spectral theorem

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

Measurement: Quantum State and Observables

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

Quantum Mechanics Basics

Covers the basics of quantum mechanics, focusing on Hamiltonian operator and Schrödinger equations.

Hermitian Operators and Spectral Theorem

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

Linear Algebra: Quantum Mechanics

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

Adjoint of Linear Operators on Inner Product Spaces

Explores the adjoint of linear operators on inner product spaces, including self-adjoint, unitary, and normal operators.

Linear Algebra: Vector Spaces & Operators

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

Linear Operators: Motivation in Quantum Mechanics

Explores the motivation for studying linear operators in Quantum Mechanics, emphasizing their essential role and practical applications.

Linear Algebra: Eigenvalues and Eigenvectors

Explores eigenvalues, eigenvectors, diagonalization, and spectral theorem in linear algebra.

Symmetric Linear Operators

Explores symmetric linear operators, eigenvalues, and eigenvectors in functional analysis.

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.

Functional Analysis I: Norms and Bounded Operators

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

Quantum Mechanics and Linear Algebra

Covers Hermitian and Unitary operators, real number equivalents, and eigenvalues.

Linear Algebra: Quantum Mechanics

Covers the application of linear algebra concepts to Quantum Mechanics, including spectral theorem and Brillouin zone.