2023-2024 / PHYS2012-1

Relativistic quantum mechanics and relativistic statistics


20h Th, 5h Pr

Number of credits

 Master in physics (120 ECTS)4 crédits 
 Master in space sciences (120 ECTS)3 crédits 
 Master in physics (60 ECTS) (Registrations are closed)4 crédits 


Peter Schlagheck

Language(s) of instruction

French language

Organisation and examination

Teaching in the first semester, review in January


Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

The aim of this course is to familiarize the student with relativistic quantum mechanics. It essentially covers the relativistic wave equations (Klein-Gordon, Dirac, Maxwell) for spin 0, spin 1/2 or spin 1 particles. It is explained through the formalism of second quantization how such equations imply a bosonic or fermionic character of the associated particles.
Topics of the course in detail: - special relativity - Maxwell's equations - quantization of fields - Klein-Gordon equation - Dirac equation - Pauli equation and its relativistic corrections

Learning outcomes of the learning unit

Principal objectives of this course: - to understand the notion of relativistic covariance and its implications - to get familiarized with the fundamental equations (Maxwell/Klein-Gordon and Dirac) that govern the dynamics of the elementary particles in our universe - to understand the association of the (integer or half-integer) spin with the (bosonic or fermionic) statistics of a particle - to understand how non-relativistic quantum mechanics emerges as limiting case of relativistic quantum mechanics - to prepare for the course "Quantum field theory"

Prerequisite knowledge and skills

Having followed an introductory course on non-relativistic quantum mechanics

Planned learning activities and teaching methods

The course will be given ex cathedra on the blackboard.

Mode of delivery (face to face, distance learning, hybrid learning)

Face-to-face course

Recommended or required readings

Recommended literature: - J. Bjorken & S. Drell: "Relativistic Quantum Mechanics" (McGraw-Hill, 1964) - A.S. Davydov: "Quantum Mechanics" (chapter VIII) (Pergamon, 1965) - W. Greiner: "Relativistic Quantum Mechanics: Wave Equations" (Springer 1987) - L.D. Landau & E.M. Lifshits: "Relativistic Quantum Theory" (Pergamon, 1971)

The evaluation will be done by an individual oral exam of 30 minutes on the contents of the course.

Work placement(s)

Organisational remarks and main changes to the course


Peter Schlagheck Département de Physique Université de Liège IPNAS, building B15, office 0/125 Sart Tilman 4000 Liège Phone: 04 366 9043 Email: Peter.Schlagheck@ulg.ac.be http://www.pqs.ulg.ac.be

Association of one or more MOOCs

Items online

lecture notes
lecture notes