Lectures related to Linear Algebra: Unitary Operators

Linear Operators: Basis Transformation and Eigenvalues

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

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.

Matrix Representation of Operators and Basis Transformation

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

Quantum Mechanics: Postulates and Observables

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

Eigenvalue problem: Eigenbasis, Spectral theorem

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

Spectral Decomposition of Unbounded Operators

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

Linear Operators: Quantum Mechanics and Linear Algebra

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

Hermitian Operators and Spectral Theorem

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

Common Orthonormal Eigenbasis to Normal Commuting Operators

Discusses the existence of a common orthonormal eigenbasis to normal operators.

Postulates of Quantum Mechanics

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

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.

Sturm-Liouville Problem: Homogeneous Boundary Conditions Essential Role

Explores the Sturm-Liouville eigenvalue problem, emphasizing the essential role of boundary conditions in ensuring self-adjointness and forming an orthogonal basis.

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.

Crash Course on Quantum Mechanics

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

Exponential of Operators and Matrices

Covers the exponential of operators and matrices, commutation properties, Jordan normal form, and linear algebra concepts related to linear operators and eigenvalue problems.

Compositions and adjoints of unbounded operators

Covers the fundamental concepts of unbounded operators and their adjoints, exploring auto-adjoint and normal operators.

Functional Calculus: Operator Definition and Properties

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

Linear Algebra: Quantum Mechanics Log in to Mediaspace to watch this video

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

Eigenvalues and Eigenvectors Log in to Mediaspace to watch this video

Covers eigenvalues and eigenvectors in linear algebra.

Linear Algebra: Quantum Mechanics Log in to Mediaspace to watch this video

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