Deepening of the concepts of quantum mechanics introduced in undergraduate course by considering condensed matter physical nano-systems. The physics describing those systems designed nowadays as nanophysics is a physics which elaborate its objects and study them based on the principles of quantum mechanics which is the fundamental background underlying the development of nanotechnologies. The concepts illustrated in this course will be the pre-requisite of many second year Master courses related to quantum engineering which allow you to start a fundamental PhD in this topic after the Master. A good knowledge in this field is also more and more essential for technological researches and development of nanodevices.

The course will be illustrated by applying fundamental principle to condensed matter quantum systems (calculation of eigenstates and their evolution, symmetry properties) and by considering examples taken from recent researches and by discussing prospects for quantum information technologies.

Bibliography: « Quantum mechanics », C. Cohen Tanoudji, Vol1, ISBN-13: 978-0471164333, Vol 2, ISBN-13: 978-0471569527.

**Outline**

**Chapter 1**: Introduction and recalls on the quantum mechanics postulates and formalism (Dirac notation, Hilbert space). Two level system, Zeeman effect, spin Hamiltonian. Tensorial product notation for states and operators. Many body quantum states (bosons and fermions). Exercices: basics of quantum mechanics formalism.

**Chapter 2**: Recalls on confinement problem: electron bound states in a potential.

Exercise: example of 1D confinement problems, quantum harmonic oscillator.

Exercices: basics of quantum mechanics formalism.

**Chapter 3**: Introduction to Atomic physics. Spherical symmetry, angular and spin kinetic momenta. Mean field approximation, central potential, many electrons atoms, Hund rules, spin orbit coupling, optical transitions.

Exercises: Grotrian diagrams, spin orbit coupling, fine and hyperfine structure.

**Chapter 4**: Approximation methods for eigenstate calculations, perturbation theory, variational method.

Exercises: application to electronic systems.

**Chapter 5**: Time evolution

General equation for the time evolution, two state systems (Rabi oscillations), perturbation theory, Fermi golden rules.

Exercises: application to electronic systems, Rabi oscillations.

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Credits: 3

Hours: 24

Code: PAX7NAAH