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Mathematical Foundations of Quantum Mechanics
Engineering & Social Sciences Program
Madrid, Spain
Dates: 1/16/25 - 6/4/25
Mathematical Foundations of Quantum Mechanics
OVERVIEW
CEA CAPA Partner Institution: Universidad Carlos III de Madrid
Location: Madrid, Spain
Primary Subject Area: Physics
Instruction in: English
Course Code: 18338
Transcript Source: Partner Institution
Course Details: Level 300, 400
Recommended Semester Credits: 3
Contact Hours: 42
DESCRIPTION
On the many pictures of Quantum Mechanics: Schrödinger, Heisenberg and Dirac. An introduction to the theory of Hilbert spaces.
Von Neumann's picture of Quantum Mechanics. The theory of operators, observables and the spectral theorem.
Perturbation theory: stationary and time-dependent perturbation theory, adiabatic theorem, semiclassical approximation, scattering theory.
Weyl's picture of Quantum Mechanics. Weyl's quantization. Coherent states and quantum optics: Wigner's transform and quantum tomography.
Feynman's picture of Quantum Mechanics. The double slit experiment. Feynman's path integral and Dirac's Lagrangian description of Quantum Mechanics.
From particles to fields.
The measurement problem in Quantum Mechanics. Measurement and reversibility. Quantum cloning. Quantum Zeno effect. The nature of quantum states.
EPR. Bell inequalities. Quantum non-locality
Von Neumann's picture of Quantum Mechanics. The theory of operators, observables and the spectral theorem.
Perturbation theory: stationary and time-dependent perturbation theory, adiabatic theorem, semiclassical approximation, scattering theory.
Weyl's picture of Quantum Mechanics. Weyl's quantization. Coherent states and quantum optics: Wigner's transform and quantum tomography.
Feynman's picture of Quantum Mechanics. The double slit experiment. Feynman's path integral and Dirac's Lagrangian description of Quantum Mechanics.
From particles to fields.
The measurement problem in Quantum Mechanics. Measurement and reversibility. Quantum cloning. Quantum Zeno effect. The nature of quantum states.
EPR. Bell inequalities. Quantum non-locality