Quantum Mechanics: Mathematical Framework

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Related lectures (30)

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Bounded Operators: Theory and Applications

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

Quantum Mechanics Basics

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

Linear Operators: Basis Transformation and Eigenvalues

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

Linear Operators: Boundedness and Spaces

Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.

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.

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.

Functional Analysis I: Spectral Theorem

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

Linear Algebra: Quantum Mechanics

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

Postulates of Quantum Mechanics

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

Weak Formulation of Elliptic PDEs

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.