Unbounded operator

Related lectures (32)

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

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

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

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

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

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

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

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

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

Introduces the need for a mathematical framework to describe linear operators on infinite-dimensional Hilbert spaces in quantum mechanics.