Dynamical Approaches to Spectral Theory of Operators

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Linear Operators: Basis Transformation and Eigenvalues

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

Introduction to Quantum Chaos

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Quantum Mechanics Basics

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

Quantum Mechanics: Postulates and Observables

Explains the postulates of quantum mechanics and the representation of observables by operators.

Postulates of Quantum Mechanics

Explains the postulates of Quantum Mechanics, focusing on self-adjoint operators and mathematical notation.

Quantum Mechanics: Mathematical Framework

Introduces the need for a mathematical framework to describe linear operators on infinite-dimensional Hilbert spaces in quantum mechanics.

Functional Analysis I: Norms and Bounded Operators

Explores norms and bounded operators in functional analysis, demonstrating their properties and applications.

Determinantal Point Processes and Extrapolation

Covers determinantal point processes, sine-process, and their extrapolation in different spaces.

Bounded Operators: Theory and Applications

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

Functional Analysis I: Spectral Theorem

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