Functional Calculus: Self-Adjoint Operators

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

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

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

Explores Hermitian operators, auto-adjoint properties, and spectral theorems in Hermitian spaces.

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

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

Explores the spectral decomposition of non-bounded operators and presents the spectral theorem for self-adjoint non-bounded operators.

Covers the basics of quantum mechanics, focusing on Hamiltonian operator and Schrödinger equations.

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

Covers properties and theorems related to compact and relatively compact operators, including the RAGE theorem and the Kato-Rellich theorem.