Quantum physics

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Introduction à la mécanique quantique II

This course is the continuation of the first semester course "Introduction to quantum mechanics I".

We will treat the quantum mechanics of a particle in three spatial dimensions which will lead us in particular to the study of angular momentum in general which in turn is closely relates to the rotations of space. We will study central potential problems in general and the hydrogen atom in particular. The addition of angular momenta is discussed. We treat the quantum mechanics of a charged particle in an electromagnetic potential in some detail with emphasis on the notion of gauge invariance. The relativistic Dirac equation and its non-relativistic limit is briefly mentioned to obtain the correct coupling of the magnetic moment of spin 1/2 particles to a magnetic field. Symmetrisation and anti-symmetrisation for identical bosons and fermions is discussed and the second-quantised formalism is mentioned. The lecture ends with a discussion of the role of symmetries and the associated selection rules.

Atoms and Photons

This lecture aims at the description of the interaction between quantum matter in its simplest form, an atom, and an electromagnetic field. A semi-classical approach, where the field is classical, is first considered, including relaxation of the atom. We then study the quantization of the electromagnetic field and its relaxation, before its interaction with an atom is described in a full quantum model.

Quantum matter

The goal of this course is to introduce somewhat "advanced" topics in quantum matter, tackle truly quantum-entangled, strongly interacting, phases of matter and materials, and present how quantum matter is a particularly rich field, with many open theoretical problems.

Statistical Field Theory and applications

This course is about how to describe complex systems using ideas of the renormalization group (‘coarse-graining’) and statistical field theory.

Master Quantum Engineering

PSL’s quantum engineering programme is a 2-year program that provides cutting-edge training. It is spread over two years and 120 ECTS, requesting full-time studies.

Quantum technologies are a strategic global topic for academia and industry. These disruptive technologies have the potential to revolutionise the design and implementation of information and communication sciences and technologies. France is investing nearly €2 billion in this field over the next four years.

A new interdisciplinary training programme in quantum technologies has been launched by PSL University in September 2022. It results from an unprecedented synergy between some of its founding schools, namely: Ecole normale supérieure, ESPCI Paris, Mines Paris, École nationale supérieure de Chimie de Paris - PSL and the Observatoire de Paris, and it is part of PSL’s graduate programme in physics.

The academic year is divided into two semesters.