Theory of Bounded Operators on Hilbert Space

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Quantum Mechanics: Spectral Basis and Schrödinger Equation

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

Spectral Decomposition of Unbounded Operators

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

Hermitian Operators and Spectral Theorem

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

Translation Groups on [0,1]

Covers the study of translation groups on the interval [0,1] with different phases and the Riesz representation theorem on Hilbert space.

Postulates of Quantum Mechanics

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

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.

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.

Eigenvalue problem: Eigenbasis, Spectral theorem

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

Compositions and adjoints of unbounded operators

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

Crash Course on Quantum Mechanics

Offers a crash course on quantum mechanics, covering vector spaces, superposition, observables, and self-adjoint operators.