Concept

Self-adjoint operator

Related lectures (32)

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

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

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

Covers the essential concepts of adjoint operators, spectrum, and resolvent sets in operator theory.

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

Covers the criteria for operators to be self-adjoint and the Friedrichs extension theorem.

Explores operator, density matrix, subsystems, states, and system evolution in quantum physics.

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

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

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

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

Covers the states of composite systems in Hilbert space, including operators, observables, tensor products, eigenvalues, and partial measurements.

Covers quantum eigenfunctions and the importance of A and B commuting for the same set of eigenfunctions.

Covers the fundamental concepts of unbounded operators in quantum physics, focusing on defining a functional calculus and spectral decomposition.

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

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

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

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

Explores convolution properties, heat equation application, and Fourier transform on tempered distributions.

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