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Quantum Mechanics: Mathematical Framework
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Related lectures (30)
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.
Normed Spaces
Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.
Quantum Mechanics: Postulates and Observables
Explains the postulates of quantum mechanics and the representation of observables by operators.
Linear Operators: Quantum Mechanics and Linear Algebra
Explores the role of linear operators in Quantum Mechanics and linear algebra, emphasizing eigenvalues and basis transformations.
Extension of Linear Transformations
Covers the extension of bounded linear transformations and the free propagator in L^2 spaces.
Measurement: Quantum State and Observables
Discusses measurement in Quantum Mechanics, focusing on state vectors, observables, eigenvalues, and probabilities.
Quantum Mechanics: Measurement
Covers the axioms of quantum mechanics and the measurement of quantities in a quantum system.
Linear Maps and the Duality Principle in Mathematics
Covers the duality principle in linear algebra and its implications in mathematics.
Segal CFT: Hilbert Space Applications
Covers the applications of Segal's Conformal Field Theory in Hilbert spaces.
Crash Course on Quantum Mechanics
Covers fundamental concepts in quantum mechanics, including vector spaces, superposition, observables, and inner product.
Linear Algebra: Quantum Mechanics
Explores the application of linear algebra in quantum mechanics, emphasizing vector spaces, Hilbert spaces, and the spectral theorem.
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