Self-adjoint operator

Related lectures (32)

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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.