Spectral Decomposition of Unbounded Operators

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Sturm-Liouville Problem: Homogeneous Boundary Conditions Essential Role

Explores the Sturm-Liouville eigenvalue problem, emphasizing the essential role of boundary conditions in ensuring self-adjointness and forming an orthogonal basis.

Functional Calculus: Self-Adjoint Operators

Covers self-adjoint operators, Weyl criterion, and functional calculus in the context of symmetric operators and real spectrum.

Compact Operators: Properties and Theorems

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

Linear Algebra: Quantum Mechanics

Explores the application of linear algebra in Quantum Mechanics, emphasizing its importance in understanding materials properties.

Bounded Operators: Theory and Applications

Covers bounded operators between normed vector spaces, emphasizing the importance of continuity and exploring applications like the Fourier transform.

Postulates of Quantum Mechanics

Explores the postulates of Quantum Mechanics, emphasizing the state of a system as a complex-valued vector in a Hilbert space.

Measurement: Quantum State and Observables

Discusses measurement in Quantum Mechanics, focusing on state vectors, observables, eigenvalues, and probabilities.

Functional Analysis I: Spectral Theorem

Covers the spectral theorem, orthanormal sequences, and bounded linear operators in Hilbert spaces.

Postulates of Quantum Mechanics

Explores the postulates of Quantum Mechanics, including states, observables, composite systems, Schrödinger equation, and entangled states.

Properties of the Spectrum

Explores the properties of the spectrum of an operator in L(H), including compactness and spectral radius.