Compact Operators: Properties and Theorems

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

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.

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

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.

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.

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

Explores spectral basis, Schrödinger equation, unitary equivalence, and self-adjoint operators.