PHY1222 : Mécanique Quantique

Special news appear here.


As a complement to the courses PHYS 1111, PHYS 1112 and PHYS 1211 which establish the bases of classical mechanics, special relativity, electromagnetism and wave physics, the aim is to expose the student to the conceptual and physical bases of the quantum description of the microscopic world. This course is 45h (lectures) +30h (tutorials) and it is worth 5 credits. Lectures are given in English.

Timetable and location

Lectures are given for 14 weeks starting on Wed, 28th of January, three hours per week. Tutorials are given on Fridays afternoons, for two hours.

  • Wed - from 8:30 to 10:30 in CYCL07 (lectures)
  • Thu - from 14:00 to 15:00 in CYCL09 (lectures)
  • Fri - from 16:15 to 18:15 (even weeks), from 14:00 to 16:00 (odd weeks) in CYCL09 (tutorials)


  • Discovery and observation of quantum phenomena in the microscopic world
  • The notion of a probability amplitude
  • Linear superposition and the Heisenberg principle
  • The Schrödinger equation
  • Examples of Solutions
  • The tunnel effect
  • Physical applications
  • Quantization of angular momentum


The literature on Quantum Mechanics is vast and it is easy to get lost. The course is based on the syllabus by Prof. Jacques Weyers which will be followed in the lectures and made available on the web. Hereafter, I only mention a few books, which might be used as references and/or for exercises:

  • D. J. Griffiths, Introduction to Quantum Mechanics, ed. Pearson , [Grif]
  • J. J . Sakurai, Modern Quantum Mechanics, ed. Addison-Wesley, [Saku]
  • S. Gasiorowitz, Quantum Physics, ed. John Wiley and Sons [Gasi]
  • R. P. Feynman , The Feynman Lectures on Physics, vol III , ed. Addison Wesley [Feyn]
  • R.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals , ed. McGraw-Hill Book Company [FeHi]

More info

This is a collection of complementary information on Quantum Mechanics that you might enjoy!

  • R. P. Feynman , The strange theory of light and matter , ed. Princeton University Press.
    Videos of four lectures on which the book is based from the University of Auckland (New Zealand), 1979.

  • Is the moon there when nobody looks? Reality and the quantum world. David Mermin (1985).

  • SPINS: a software for playing with spin sequential measurements.
    Very nice lectures notes (pdf) on QM based on the spin measurements by David H. McIntyre.

Training material

The complete Syllabus

Here the pdf file with several exercises is given.

Here the pdf file with examples of the theory questions which will appear in the exam.

Here A short note on the derivation of the free-particle propagator.


Exam given on the 21st of August 2007.

Exam given on the 5th of June 2007.

Exam Simulation given on the 9th of May 2007.


The superposition principle and the general solutions.



Lectures & Tutorials





Wed 28 Jan
Thu 29 Jan

The microscopic world:
The limits of classical physics.

[Gasi], Chapter I

Lecture notes: Chapter I

Fri 1 Feb

No Exercises




Wed 4 Feb
Thu 5 Feb

The microscopic world:
The limits of classical physics.

[FeHi], Chapters I & II

Lecture notes: Chapter II

Fri 6 Feb

Exs: 1,8,9,10,11,12

Due Homework:
Exs: 1,4,8,9,12




Wed 11 Feb
Thu 12 Feb

The principles of Quantum Mechanics.
The double-slit experiment. Identical particles

[FeHi], Chapters I & II

Lecture notes: Chapter II

Fri 13 Feb

Quiz 1. Further discussion on the exercises of the previous week and Exs: 13,14,15,16

No homework due




Wed 18 Feb
Thu 19 Feb

The classical limit. Derivation and properties of the Schrodinger Equation. Operators in QM: position and momentum. Correspondence principle and Ehrenfest theorem.

Lecture notes: Chapter III

Fri 20 Feb

Tutorial: Exercises 18 and 19.

No homework due
Solutions Ex. 18 and 19




Wed 25 Feb
Thu 26 Feb

Time-independent Schrodinger equation and stationary states.The Hamiltonian operator.
Density and Current. Free Particle.

Lecture notes: Chapter III Chapter IVa

Fri 27 Feb

Tutorial: Discussion of the symmetric box

Due Homework: symmetric box




Wed 4 Mar
Thu 5 Mar

Density and Current. Free particle.
Scattering in QM: Potential step. Potential barrier and tunnel effect.

Lecture notes: Chapter IVa

Fri 6 Mar






Wed 11 Mar
Thu 12 Mar

Scattering exercises and the delta-function.

Lecture notes: Chapter IVa

Fri 13 Mar

Quiz 2





Wed 18 Mar
Thu 19 Mar

The harmonic oscillator in one and two dimensions.

Lecture notes: Chapter IVb

Fri 20 Mar

Tutorial: Quiz





Wed 25 Mar
Thu 26 Mar

Hilbert spaces. Hermitian operators and their spectrum.

Lecture notes:
Chapter V

Fri 27 Mar






Wed 1 Apr
Thu 2 Apr

Lecture notes:
Chapter V

Fri 3 Apr






Wed 22 Apr
Thu 23 Apr

Lectures: Uncertainty relations

Lecture notes: Chapter VI

Fri 24 Apr






Wed 29 Apr<\br>Thu 30 Apr

Lectures: Uncertainty relations (continued).

Lecture notes: Chapter VI

Fri 1 May






Wed 6 May
Thu 7 May

Lectures: momentum space representation.

Lecture notes: Chapter VII

Fri 8 May






Wed 13 May
Thu 14 May

Lectures: The variational principle and the WKB approximation.


Fri 15 May