Compact operator on Hilbert space

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Postulates of Quantum Mechanics

Introduces the postulates of Quantum Mechanics, focusing on states in a Hilbert space and the role of observables.

Spectral Theorem: Second

Covers the spectral theorem, focusing on the second part and orthonormal sequences in a separable Hilbert space.

Linear Operators: Basis Transformation and Eigenvalues

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

Unitary Group and Spectral Types

Covers the proof of unitary group uniqueness and spectral types.

Symmetric Linear Operators

Explores symmetric linear operators, eigenvalues, and eigenvectors in functional analysis.

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.

Function Spaces: Review and Compact Operators

Covers the review of function spaces and explores the concept of compact operators.

Hydrogenic Atom Stability

Covers the proof of the Coulomb uncertainty principle and the stability of hydrogenic atoms.

Spectral Theorem for Operators

Explores the spectral theorem for operators in a Hilbert space.

Separation Criterion in Recollement

Focuses on a criterion for separability in recollement, demonstrating iron properties and applications in various cases.