At the end of the teaching unit, the student will be able to understand the basic concepts of quantum physics (quantum, measurement, entanglement, spin) and use them with the appropriate formalism. He will be able to explain the historical results of quantum physics and recent applications (cryptography, quantum computer, etc.)
Situate quantum mechanics in the historical context of the development of physics.
Use the formalism of quantum mechanics wisely, based on the postulates.
Highlight purely quantum concepts (entanglement, spin) and their links with classical physics and with recent applications (cryptography, quantum computer).
The course provides an introduction to quantum concepts. After a historical overview, the mathematical tools of quantum physics are introduced. The postulates of quantum theory are then presented. Finally, purely quantum concepts (spin, localization, entanglement) are explained and their consequences for understanding the world and technology are highlighted.
1 The quanta
1.1 Light and photons
1.2 Matter and quanta
2. Schrödinger equation and first consesuances
2.1 The wave function and Schrödinger equation
2.2 Wave paquets and particles
2.3 Stationnary states and state superpositions
2.4 Quantum wells and barriers at 1D
2.5 Boundary conditions
2.6 Examples of 1D systems
3 Mathematical tools
3.1 State space, scalar product and Dirac Notation
3.2 Operators and observavbles
3.3 Complete set of commuting operators
3.4 Representations . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Wave mechanics and matrix mechanics
3.6 Tensorial product of space states
4 Postulates and their consequences
4.1 State of a system
4.2 Physical quantities and observables
4.3 Result of a measurement
4.4 probability of measurement
4.5 Projection
4.6Time evolution
.
5 Statistical description of QM
5.1 Statistical indicators
5.2 Heisenberg Inegality
5.3 Evolution of the mean value of an observable .
5.4 Density matrix and operator
6 Other purely quantum concepts
6.1 The view of Schrödinger, Heisenbert and Interaction
6.2 Classical Limits and Ehrenfest theorem
6.3 The spin
6.4 Determinism, locality, Intrication and hidden variables
6.5 Information, communication et Quantum Computer
Lectures and pratical work with participation of the students.
Oral exam with an written preparation. The students have form provide by the teacher.
C. Cohen-Tannoudji, B. Diu et F. Laloë, Mécanique quantique I (Editions Hermann, Collection : Enseignement des sciences, 1997)
\textit{Mécanique Quantique}(2 tomes),
N. Zettili. Quantum mechanics. Wiley (2003)
B.H. Bransden, C.J. Joachain. Quantum Mechanics.Pearson Education (2000)
C. Aslangul. Mécanique Quantique(2 tomes), De Boeck - Larcier (2007)
J.-P. Pérez, R. Charles, O. Pujol. Quantique. Fondements et applications.De Boeck (2013)
J.-M. Levy-Leblond, F. Balibar. Quantique, Rudiments. Interédition (1984)
| Training | Study programme | Block | Credits | Mandatory |
|---|---|---|---|---|
| Bachelor in Physics | Standard | 0 | 5 | |
| Bachelor in Physics | Standard | 2 | 5 |