Functional Calculus: Self-Adjoint Operators

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Essential Operators: Spectrum and Resolvent Set

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

Quantum Mechanics: Postulates and Observables

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

Linear Operators: Basis Transformation and Eigenvalues

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

Postulates of Quantum Mechanics

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

Dynamical Approaches to Spectral Theory of Operators

Explores dynamical approaches to the spectral theory of operators, focusing on self-adjoint operators and Schrödinger operators with dynamically defined potentials.

Herglotz Representation Theorem

Covers the Herglotz representation theorem and the construction of projection-valued measure.

Theory of Bounded Operators on Hilbert Space

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

Compositions and adjoints of unbounded operators

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

Self-Adjoint Operators

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

Quantum Mechanics: Spectral Basis and Schrödinger Equation

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