Spectral Theory: Friedrichs Extension Theorem

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

Covers the concept of the spectrum in quantum physics, including invertibility, eigenvalues, and observables.

Explores the spectral theory of non-bounded operators and the importance of closed operators for spectral decomposition.

Reviews Dirac notation, observable operators, and exact TDSE solutions using basis sets and Hamiltonians.

Explores spin operators in quantum chemistry, focusing on their properties and commutation rules with orbital angular momentum operators.

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

Covers quantum eigenfunctions and the importance of A and B commuting for the same set of eigenfunctions.

Covers the transmission operator, commutation relations, position representation, momentum eigenstates, and Fourier transform properties.

Explores the quantum effective action, its role in perturbation theory, and the organization of correlators in momentum space.

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