## Objectifs

The goal of this course is to introduce the fundamental principles of quantum physics, which are needed to understand the theoretical and experimental basis of modern science and technology including materials science, electronics, quantum chemistry, quantum engineering, nanotechnology and photonics. The course emphasizes conceptual understanding but also relies on the necessary amount of mathematical formalism, which is essential for understanding quantum mechanics. Numerous examples of practical use of quantum mechanics are given during the lectures and are studied in more details in preceptorship sessions. Tutorial classes allow the students to put into practice the concepts seen during the lectures.## Syllabus

- Introduction to quantum physics

- Waves mechanics

- General formalism of quantum Mechanics

- The postulates of quantum mechanics

- Perturbation theories

- Harmonic oscillator

- Angular Momentum

- Hydrogen atom

- Addition of two angular momentums

- Quantum statistics

## Tutorials

- Rectangular potential barrier, the infinite and finite quantum wells

- The parity operator

- Application of the measurement postulate

- Harmonic oscillator with a stationary perturbation and with a time-dependent perturbation

- Spin in a rotating frame, Nuclear Magnetic Resonance

- Interaction between two spins

- Addition of two spins

## Preceptorship

Preceptorship sessions will deal with numerous areas of contemporary physics, both fundamental and applied, where quantum mechanics plays a major role.

- Wave-particle duality. Application to matter probes and to atom-scale optics.

- Colour centres in ionic crystals (F-centres).

- WKB method. Application to the tunnel effect and the Gamow alpha emission model.

- Formation of interstellar molecular hydrogen.

- Neutron interferometry. Application to spin rotation and gravitational effect.

- Factorisable quantum states, entangled quantum states. Application to quantum cryptography and to principles of qubit teleportation.

- The NH3 MASER.

- Zeeman effet and Stark effect on hydrogen atom.

- Superconducting quantum bit.

**Requirements :**Classical physics: mechanics and electromagnetism. Mathematics: vector spaces, matrices, differential equations.

**Evaluation mechanism :**Written examination.

**Last Modification :**Wednesday 31 May 2017