Advanced Quantum Mechanics

Code:

F4034

Acronym:

F4034

Keywords
Classification	Keyword
OFICIAL	Physics

Instance: 2023/2024 - 1S

Active?	Yes
Responsible unit:	Department of Physics and Astronomy
Course/CS Responsible:	Master in Physics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:A_ASTR	7	Study plan since academic year 2023/2024	1	-	6	42	162
			2
M:F	12	Official Study Plan	1	-	6	42	162

Teaching language

English
Obs.: opcionalmente em Português, se todos os estudantes dominarem a língua

Objectives

To acquire knowledge, skills, and methods to facilitate the assimilation of results from the literature in Particle Physics, Condensed Matter Physics, Quantum Optics, Astrophysics, etc.

To know and to be able to apply the basic techniques of problem formulation and calculations in Quantum Physics: basis changes, use of symmetries, perturbation theory, second quantization, field quantization, relativistic wave equations.

To become proficient in quantum mechanical problem solving.

Learning outcomes and competences

Practical skills and consolidated knowledge on quantum theory. These will enable independent study of research literature in areas such as particle physics, condensed matter physics, quantum optics, etc., as well as undertaking independent research in those areas.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

A previous quantum mechanics course (tipically 2 semesters covering a standard syllabus on undergraduate quantum mechanics).

Program

1. Review of quantum-mechanical formalism — Mathematical structure of quantum mechanics. Physical content of the theory. Density matrix. Compound systems and product spaces. Time evolution.

2. Path integral formulation of quantum mechanics — The path integral, simple applications and equivalence to the conventional formulation.

3. Symmetry, its consequences and applications — Symmetries of the Hamiltonian and spectral consequences. Infinitesimal transformations, generators, conserved quantities. Discrete and continuous symmetries. Quantum numbers. Rotational symmetry, angular momentum, spin. Addition of angular momenta and irreducible representations. Tensor operators and Wigner-Eckart theorem. Examples and applications.

4. Many-particle systems and second quantization — Indistinguishability and the symmetrization postulate. quantization of coupled oscillators, normal modes and bosons. Fock space. Fermions. Representation of operators in second quantization. Examples and applications.

5. Electromagnetic radiation — Quantization of the electromagnetic field. Photons, radiation states, classical limit. Interaction of radiation and matter in the dipole approximation. Selection rules. Examples and applications.

6. Introduction to relativistic quantum mechanics: wave equations — Relativistic notation, symmetry aspects. The dirac equation. Non-relativistic limit of the Dirac equation coupled to electromagnetic fields, spin-orbit interaction. The Klein-Gordon equation.

Mandatory literature

J. J. Sakurai; Modern quantum mechanics. ISBN: 9780321503367
Bipin R. Desai; Quantum mechanics with basic field theory. ISBN: 978-0-521-87760-2
Baym Gordon; Lectures on quantum mechanics. ISBN: 0-8053-0667-6
Walter Greiner; Relativistic quantum mechanics. ISBN: 3-540-50986-0

Complementary Bibliography

Walter Greiner; Quantum mechanics. ISBN: 3-540-58080-8 (Volume "Symmetries")
Walter Greiner; Quantum mechanics. ISBN: 3-540-60073-6 (Volume "Special Chapters")

Teaching methods and learning activities

Lectures where the topics are presented and examples or problems are discussed. The lectures are complemented with self-study by the students to consolidate and delve further into the topics covered.

Self-practice where students working through problem sets distributed periodically.

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Teste	100,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	120,00
Frequência das aulas	42,00
Total:	162,00

Eligibility for exams

Cannot be absent to more than 25% of the scheduled lectures. Attendance will be registered.

Calculation formula of final grade

Final score = max(T1 + T2, ER).

The final score can be obtained in two ways: (1) by submitting to evaluation in 2 tests (T1 e T2) distributed throughout the semester; or (2) by sitting for the final exam (ER) only, which takes place in the recourse examination period (“época de recurso” in portuguese).

Each test (T1 and T2) has a total score of 10 points. The first test (T1) will take place midterm and the second (T2) takes place in the normal examination period.

Students who have been evaluated in the tests T1 and T2 but wish to improve their final score, can do so by sitting for the final recourse examination. In this case, the best of the scores will prevail, as summarized in the above formula for the final score.

Classification improvement

By attending the unit and submitting to the two evaluation tests, or by sitting for the final exam in the recourse examination period (“época de recurso”), in accordance with the Regulation for the Evaluation of Students at FCUP.

Observations

Course unit evaluation panel (júri): Vítor M. Pereira, Eduardo Castro.