Quantum Mechanics


Quantum Mechanics is undoubtedly one of the most beautiful creations of the human mind in the XX century. Being part of the continuous search for the truth and the understanding of the real world, this construction, laboriously built along a few decades by some of the greatest physicists of the time, shoed itself as a consistent theory that allowed for the interpretation of existing experimental results and previewed other. Knowledge of contemporary physics, even at a not too high level, asks for acquisition of the basis of quantum mechanics.

In this course, the student will acquire the fundamental concepts where lies the quantum treatment of a large number of problems of modern physics.

After approval in this course, the student will be able to deal with both theoretical and applied problems that will ask for a quantum theory basis.

The mathematical methods that will be used, mostly in the algebra domain, should have been acquired beforehand, but will be reviewed.

General characterization





Responsible teacher

José Paulo Moreira dos Santos


Weekly - 5

Total - 65

Teaching language



Previous approval in the following courses: Análise Matemática I, II e III, Física I, II, III, and IV, A.L.G.A. and Vibrations and Waves.


  • Notes written by the instructor.
  • F. Duarte Santos, A. Amorim, J. Batista, Mecânica Quântica, Fundação Calouste Gulbenkian, Lisboa, 2008.
  • W. Greiner, Quantum mechanics: an introduction, Springer-Verlag, Berlin, 1994.
  • S. Gasiorowicz, Quantum Physics, 2nd Ed., John Wiley and Sons, New York, 1996.
  • C. Cohen Tannoudji, B. Diu et F. Laloë, Quantum mechanics, John Wiley & Sons, 1991.
  • J. P. Santos e M. F. Laranjeira, Métodos Matemáticos para Físicos e Engenheiros, Fundação da Faculdade de Ciências e Tecnologia, Lisboa, 2004.

Teaching method

The course is organized in lectures where the theory is presented, and recitation sessions where problems are discussed with the instructor.

Evaluation method


Subject matter

  1. Historical introduction
  2. From classical to quantum
  3. The mathematics of Quantum Mechanics
  4. The postulates of Quantum Mechanics
  5. Study of unidimensional simple systems
  6. Particle scattering and barrier penetration
  7. Systems of particles
  8. The Schrödinger equation in three dimensions
  9. Angular momentum
  10. Quantum states in three dimensions
  11. Methods of approximation - perturbation theory
  12. Quantum computing