SPOCs available at Sorbonne University - 3P001
Quantum Mechanics - 3P001
Quentin Glorieux, Thibaut Jacqmin, Emily Lamour
French
English
Educational team The teachers in charge of this course are Emily Lamour, professor at INSP (Institut des NanoSciences de Paris) (lamour@insp.upmc.fr) and Thibaut Jacqmin (thibaut.jacqmin@lkb.upmc.fr), associate professor at LKB (Laboratoire Kastler Brossel).
This course lays the foundations of quantum mechanics, from wave function to quantum gates.
Full course description After introducing the historical perspectives on quantum mechanics, we will introduce the Schrodinger formalism to describe fascinating phenomenon such as tunnel effect, one particle duality and quantum wells. In the second part we will review the Dirac formalism and the postulates of quantum. Applying this formalism to two-level system and quantum harmonic oscillator, we will study Rabi oscillations and opto-mechanics. Finally we will introduce the spin and Bloch sphere for application in MRI and quantum computing (Bell inequalities). Domain Physics
Prerequisites Wave Physics: • Monochromatic plane waves, group and phase velocity • Interference, phase-coherence • Far-field diffraction (Fraunhofer diffraction) • Standing waves
If you have already heard about the following concepts, it will help: • Notion of photon, wave-particle duality, de Broglie wavelength • Polarization of a single photon • Wave-packet, Heisenberg inequality
Regarding Mathematics, basic knowledge in linear algebra and analysis are required: • Complex notation • Hilbert space: vectors, matrices, linear applications, dual space. • Diagonalization of 2x2 and 3x3 matrices. • Differential equations (1st and 2nd order) • Fourier transform: a useful tool in quantum mechanics (as in physics in general).
Note that the first tutorial will be about Fourier transforms and the Dirac distribution, to make sure that everyone acquires those very important tools.
Course structure Part 1 Week 1 - The quantum revolution Week 2 - The time independent Schrödinger equation Week 3 - Bound states and quantum well Part 2 Week 4 - The principles of Quantum Mechanics Week 5 - Observables and commutation Week 6 - Harmonic oscillator in Dirac's formalism Week 7 - Continuous basis, x and p representations Part 3 Week 8 - Simple two-level systems Week 9 - Spin 1/2 Week 10 - Qubit ans entanglement Week 11 - Quantum information Week 12 - Quantum information Complements Week 13 - Angular momentum Week 14 - The Hydrogen atom
All the written documents of this course are available in English.
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Level Bachelor (3rd year)
Number of credits 6 ECTS
French with english subtitles |
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