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Advanced Quantum Mechanics

Advanced Quantum Mechanics

Code	17537
Year	1
Semester	S1
ECTS Credits	6
Workload	TP(60H)
Scientific area	Physics
Entry requirements	None
Learning outcomes	Students will learn some topics, methods and applications of Advanced Quantum Mechanics. Namely: - Operator methods, interaction picture, and the importance of gauge symmetries. - Functional methods and path integral formulation. - Many-particle systems. - Concepts of quantum information.
Syllabus	1. Quantum mechanics topics Harmonic oscillator and creation-annihilation operators Mixed states, density operator and partition function Evolution operator Schrödinger, Heisenberg and interaction pictures Gauge invariance 2. Functional Methods and Path Integral Formulation Propagator Path integral in configuration space and phase space Free particle Harmonic oscillator 3. Many-particle systems Bosons and fermions Creation-annihilation operators, occupation numbers and Hilbert space Field operators Green's functions of a particle: definitions and properties Application to strongly degenerate electron gas 4. Quantum information Entangled states Qubits Quantum information Introduction to quantum computing
Main Bibliography	Claude Cohen-Tannoudji, Bernard Diu, Franck Laloë - Quantum Mechanics, 2.ª edição, Wiley (2019) J. J. Sakurai, Jim Napolitano - Modern Quantum Mechanics, Cambridge University Press 2020 Hagen Kleinert - Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, World Scientific (2009) A. L. Fetter, J. D. Walecka - Quantum Theory of Many-Particle Systems, McGraw-Hill (2003) M Le Bellac, A Short Introduction to Quantum Information and Quantum Computation, Cambridge University Press (2006)
Language	Portuguese. Tutorial support is available in English.