Phelma Formation 2022

Quantum physics II - 4PMNPQ27

  • Number of hours

    • Lectures 22.0
    • Projects 0
    • Tutorials 16.0
    • Internship 0
    • Laboratory works 0


    ECTS 2.5


This second course in quantum mechanics will deepen the physical concepts describing the microscopic properties of materials and devices. A brief introduction to lagrangian mechanics will allow us to go into the foundations of quantum mechanics. We will then apply the tools from kinetic momenta to exactly calculate the energy levels of a charged particle in a Coulomb potential (Hydrogen atom). Going further usually requires approximations. Perturbation theory is one example of fundamental importance and its time-dependent version allows understanding transition probabilities between states (Fermi golden rule). We then use this for an introductory description of the interplay of matter and electromagnetic radiation. We conclude with a chapter on scattering theory.

Contact Clemens WINKELMANN


  • Introduction to analytical mechanics. Lagrangian, conjugate variables, hamiltonian, quantization.
  • The harmonic oscillator (exercise session).
  • Kinetic momentum in quantum mechanics. Quantum numbers, electron spin, addition of momenta.
  • Quantum description of the hydrogen atom.
  • Time-independent perturbation theory. Degenerate/non-degenerate case.
  • Time-dependent perturbation theory. Example of constant perturbation of a harmonic oscillator. Fermi golden rule.
  • Introduction to second quantization: atom in an electromagnetic field. Absorption, spontaneous/stimulated emission of photons.
  • Scattering theory.

  • Principles of quantum mechanics, Schrödinger equation
  • Dirac formalism in hermitian vector space.


Semester 7 - The exam is given in english only 

3 hours written exam, hand-written documents and photocopies allowed, no books, no calculators

session 1 = DS (3H) sans documents sauf feuille A4 manuscrite RV
session 2 = DS (3H) sans documents sauf feuille A4 manuscrite RV
session 1 confinée = DS (3H) documents autorisés
session 2 confinée = DS (3H) documents autorisés

Additional Information

Semester 7 - This course may be followed in french or in english  

Curriculum->Engineering degree->Semester 7


Mécanique quantique, tome I and II, Claude Cohen-Tannoudji, Bernard Diu, Franck Laloë

Physique Quantique, Michel Le Bellac, EDP Sciences