Spectral Decomposition of Unbounded Operators

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

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

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

Covers the proof of unitary group uniqueness and spectral types.

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

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

Delves into unitary operators, self-adjoint properties, and spectral theorems in linear algebra.

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

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

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