| Code |
17537
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| Year |
1
|
| Semester |
S1
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| ECTS Credits |
6
|
| Workload |
TP(60H)
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| Scientific area |
Physics
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|
Entry requirements |
None
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|
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.
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|
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
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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)
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Teaching Methodologies and Assessment Criteria |
The course is structured with theoretical and pratical classes – TP, where there will always be an exposition of the subjects of the course
with presentation and solving of problems related with the UC topics.
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Language |
Portuguese. Tutorial support is available in English.
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