Theory of Bounded Operators on Hilbert Space

Related lectures (32)

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

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

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

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

Covers the proof of unitary group uniqueness and spectral types.

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

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

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

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

Explores the spectral decomposition of self-adjoint operators on Hilbert spaces.