Description

The course presents an introduction to theoretical methods in Quantum Mechanics used in the practical work of a physicist, followed by an introduction to the concept of symmetries in Quantum Mechanics. Practical tools and fundamental concepts are illustrated with examples taken from atomic, nuclear, and particle physics. Elements of the “second quantum revolution”, like Bell's theorem and quantum entanglement, are presented, as well as advanced topics of Quantum Mechanics, like particle indistinguishability and exchange energy.
This course takes place in the first semester of Master 1, in coordination with the optional course “Advanced Quantum Mechanics”, where special subjects are discussed in detail. The course is a pillar for several courses of the second semester of Master 1: the two core courses “Nuclear Physics and Elementary Particles”, and “Solid State Physics”, as well as the optional courses “Relativistic Quantum Mechanics”, “Atomic and Molecular Physics”, and “Electronics for Quantum Science”.   
The course is also central to the Master 2 program that focuses on subatomic physics (Subatomic and Astroparticle Physics), as well as for those focused on quantum sciences and condensed matter (Quantum technologies, and Physics of Quantum and Soft Condensed Matter).

This Master 1 course on Quantum Mechanics is meant to be a second one on the subject. It requires an introduction covering the notions of wave-function and Schrödinger equation, the harmonic oscillator and the hydrogen atom, as well as Hilbert spaces and the Dirac notation.  

The objectives are:

• To be familiar with the basic concepts of quantum mechanics, being able to apply these concepts in physical situations that need to be modelled.
•  To be able to apply approximate methods in the solution of complex physical problems of quantum nature.
• To determine the key role played by spatial symmetries in the formulation of a physical problem and the resulting simplification in its analysis.

Compétences visées

• Applying knowledge in physics;

• Apply methods from mathematics and digital technology;

• Produce a critical analysis, with hindsight and perspective;

• Research a current physics topic using specialised resources;

• Communicate in writing and orally, including in English.

Syllabus

 •    Stationary perturbation theory. Variational methods. Time-dependent perturbations. Fermi's golden rule.

•    Symmetries in Quantum Mechanics. Rotations and their representations. Spin. Addition of angular momenta. Spin-orbit coupling.

•    Density matrix. Entanglement. Bell's theorem.

•    Indistinguishable particles. Exchange energy.

Bibliographie

• R. Shankar: Principles of Quantum Mechanics, Plenum (1980), Springer (1994).
• D.J. Griffiths, Introduction to Quantum Mechanics, Prentice Hall (1995), Cambridge (2018).
• L.D. Landau et E. Lifchitz, Mécanique Quantique, Mir (1960, 1982).
• C. Cohen-Tannoudji, B. Diu et F. Laloë, Mécanique Quantique, Hermann (1973).

Contacts

Responsable(s) de l'enseignement

• Rodolfo Jalabert

MCC

Les épreuves indiquées respectent et appliquent le règlement de votre formation, disponible dans l'onglet Documents de la description de la formation.

Régime d'évaluation

CT (Contrôle terminal, mêlé de contrôle continu)

Coefficient

1.0

Évaluation initiale / Session principale - Épreuves

Seconde chance / Session de rattrapage - Épreuves