SPOCs available at Sorbonne University - 3P001

_{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).

_{Course description}

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.

• Workload 150 hours in total

• Semester 1
• Duration - 02-09-2019 - 20-12-2019
• Deadline for registering - 02-09-2019

• Assessment :
• Midterm exam (25% final grade), final written exam (50% final grade),  + continuous assessment (25%) including assignments within the online course.
• Final exam - between 06-01-2020 - 10-01-2020
• Resit exam - between 08-06-2020 - 13-06-2020

To register

Level Bachelor (3rd year)

Number of credits 6 ECTS

 Language

French with english subtitles