UE Quantum mechanics and atomic physics

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Degrees incorporating this pedagocial element :


This course is in two parts: the first is a more in-depth exploration of the quantum mechanics concepts presented in the Physics bachelor, in particular introducing the different resolution methods. The second focuses on a detailed description of atoms.

 Quantum Mechanics part 

        - Chapter I: Introduction, reviews: assumptions, wave function and Dirac notation, operators and measurement theory, Schrödinger equation, Heisenberg uncertainty principle

        - Chapter II: Harmonic potential: harmonic oscillator (review), Schrödinger equation in the presence of a magnetic field (gauge invariance), electromagnetic field quantification

        - Chapter III:  Angular momentum: spin ½, spin Hamiltonian (precession), fermions/bosons, momentum coupling (degrees of freedom, tensor product of Hilbert spaces, Clebsch-Gordan coefficients)

        - Chapter IV:  Symmetries and conservation laws: symmetry groups (Noether's theorem), generators and degeneracy, periodic potential (Bloch), Runge-Lenz invariance in central potentials

        - Chapter V: Approximation methods: stationary (first and second order, degenerate states) and time-dependent perturbations (Fermi's golden rule, Wigner-Eckhart theorem), variational method, Wayl and Sommerfeld formulae 

        - Chapter VI: Scattering theory (part I): introduction, scattering amplitude, Born approximation

Atomic Physics part

        - Chapter VII: Hydrogen atom: review, fine and hyperfine structures, atom-photon interaction (classical/quantum), density operator, Bloch equation, systems involving several electrons (helium, Hund's rules)

        - Chapter VIII: Cold atoms: scattering (part II), modern experiments in atomic physics, Bell's inequalities 

Recommended prerequisite

Quantum Mechanics bachelor (L3) course (formalism, wave-particle duality, black-body and photons, Heisenberg uncertainty principle, Schrödinger equation, potential wells and barriers, harmonic oscillator, hydrogen atom and spin ½).