Mécanique quantique from Coursera

Comme l'ont montré de plus en plus d'expériences effectuées dès le début du vingtième siècle, les lois de la mécanique newtonienne cessent d'être valables dès qu'on tente de les appliquer à très petite échelle, celle des atomes, des molécules ou des noyaux. On entre alors dans le domaine de la mécanique quantique, où les lois physiques prennent une tout autre nature qui a pu être formalisée de manière rigoureuse à la fin des années 1920. Cette véritable révolution intellectuelle est non seulement indispensable pour comprendre la véritable nature du monde physique, des particules élémentaires au big bang, mais elle est également à l'origine de la plupart des technologies modernes comme la micro-électronique, les lasers ou les télécommunications optiques.

Ce cours constitue une première introduction à la mécanique quantique. En employant une approche historique et en s'appuyant sur une confrontation entre expériences et théorie, il vous permettra de comprendre les principes de base de la mécanique quantique et d'entrevoir quelques-unes de ses applications. Le cours se composera des huit séances ci-dessous.

1. Dualité onde-corpuscule

2. La fonction d'onde

3. Transformée de Fourier

4. De l'impulsion à l'hamiltonien

5. La particule quantique confinée

6. Mesures quantiques individuelles

7. Puis de potentiel à une dimension

8. Effet Tunnel

What's inside

Syllabus

Dualité onde-corpuscule

Dans le cadre d'une approche historique, ce chapitre vous permettra de découvrir les difficultés auxquelles la physique classique s'est trouvée confrontée au début du vingtième siècle. C'est la naissance de la théorie des quanta, avec la dualité onde-corpuscule et les interférences entre ondes de matière. Les exercices (ou travaux dirigés) vous permettront de revoir les notions de probabilités qui vous seront utiles dans la suite du cours.

La fonction d'onde

Ce chapitre introduit la notion de fonction d'onde. En suivant la démarche suivie initalement par Schrödinger, vous pourrez découvrir l'équation de Schrödinger pour une particule libre qui régit l'évolution de la fonction d'onde au cours du temps. Les travaux dirigés vous permettront de manipuler la fonction d'onde dans le cas d'interférences d'ondes de matière.

Transformée de Fourier et diffraction

Ce chapitre introduit une notion mathématique d'une grande utilité en physique, à savoir la transformation de Fourier. Son domaine d'application dépasse très largement la seule mécanique quantique, comme vous pourrez vous en rendre compte avec les expériences d'optique qui vous seront présentées. Les travaux dirigés vous permettront de manipuler les propriétés de la transformée de Fourier, avec notamment la démonstration de la relation d'incertitude de Heisenberg.

De l'impulsion à l'hamiltonien

Ce chapitre nous permettra de manipuler les opérateurs position et impulsion, ce qui nous conduira à introduire l'équation de Schrödinger dans le cas général où l'énergie potentielle de la particule sera prise en compte. Lors des travaux dirigés, vous pourrez découvrir comment se propage un paquet d'ondes en l'absence d'énergie potentielle. Nous aborderons également le problème de la stabilité de la matière, qui est incompréhensible dans le cadre de la physique classique.

La particule quantique confinée

Ce chapitre aborde la notion de mesure en mécanique quantique, problème délicat dont l'étude sera poursuivie lors du chapitre suivant. On introduira la notion d'observable associée à une grandeur physique. On montrera comment la connaissance des états propres de l'hamiltonien permet d'écrire la solution générale de l'équation de Schrödinger. Enfin, on recherchera les niveaux d'énergie dans le cas d'un puits de potentiel infini. Les travaux dirigés porteront sur le courant de probabilité et reviendront sur le calcul des niveaux d'énergie dans un puits infini.

Mesures quantiques individuelles

Ce chapitre introduit la version forte du postulat de la mesure. Les TD porteront sur les potentiels constants par morceaux. Vous aurez également à rédiger - et à corriger - un devoir portant sur l'effet tunnel.

Puits de potentiel à une dimension

Ce chapitre discute en détail les états propres d'un puits de potentiel à une dimension, avec les cas particuliers importants du puits symétrique et du puits semi-infini. Les TD porteront sur l'existence d'états liés dans un puits de potentiel à une dimension.

L'effet tunnel

Ce dernier chapitre porte sur diverses manifestations de l'effet tunnel, à savoir le microscope à effet tunnel, la radioactivité alpha et enfin le modèle du puits double, qui permet de comprendre l'origine physique de la liaison chimique ainsi que les niveaux d'énergie utilisés dans le premier MASER.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Convient aux débutants en mécanique quantique

Développe des notions fondamentales en mécanique quantique

Explore les applications de la mécanique quantique dans les technologies modernes

Apprend les principes de base de la mécanique quantique

Enseigné par des experts en mécanique quantique de l'École Polytechnique

Approche historique et expérimentale pour une compréhension approfondie

Reviews summary

Quantum mechanics: a comprehensive introduction

This course offers a solid foundation in quantum mechanics, guided by expert instructors. It approaches the subject historically, emphasizing the evolution of ideas and the interplay between theory and experiment. The syllabus covers key concepts such as wave-particle duality, the Schrödinger equation, Fourier transforms, and the quantum harmonic oscillator. Students appreciate the clear explanations, engaging examples, and challenging exercises that deepen their understanding. Overall, this course is highly recommended for anyone seeking an introduction to quantum mechanics.

Traces the historical development of quantum mechanics, making the subject more accessible.

"approche historique"

"on découvre les difficultés auxquelles la physique classique s'est trouvée confrontée au début du vingtième siècle."

"C'est la naissance de la théorie des quanta, avec la dualité onde-corpuscule et les interférences entre ondes de matière."

Engaging exercises reinforce concepts and foster deep understanding.

"Les travaux dirigés vous permettront de manipuler la fonction d'onde dans le cas d'interférences d'ondes de matière."

"Les TD porteront sur le courant de probabilité et reviendront sur le calcul des niveaux d'énergie dans un puits infini."

Highly knowledgeable and engaging professors provide clear explanations.

"Excellent !"

"Excellente formation. Très complète. Merci beaucoup."

"Cours passionnant. Un grand merci à toute l'équipe de ce MOOC."

Could go deeper into advanced topics, such as spin and the Stern-Gerlach experiment.

"J'aurai aimé qu'il aille bien plus loin avec le spin/Sterlan-Gerlach etc."

Assumes a strong mathematical background, which may be challenging for some.

"Il peut être plus détaillé dans les traitements mathématiques."

"Il ne faut pas forcément sauter les contenues mathématiques afin d'énoncer les théories plus claires."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Mécanique quantique with these activities:

Review Quantum Mechanics

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Review the postulates of quantum mechanics.
Solve problems involving the Schrödinger equation.
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Practice Quantum Mechanics Problems

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Continuously reinforce understanding of quantum mechanics principles and their applications.

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Solve practice problems on wave-particle duality.
Complete exercises involving the uncertainty principle.
Apply quantum mechanics to explain atomic and molecular phenomena.

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Career center

Learners who complete Mécanique quantique will develop knowledge and skills that may be useful to these careers:

Quantum Computer Engineer

As a Quantum Computer Engineer, you will be working on the development and application of quantum computers. This could include designing new quantum computing hardware, or developing new quantum algorithms. You will need a strong understanding of computer science, physics, and mathematics. This course will help build a foundation in quantum mechanics, which is essential for understanding the operation of quantum computers.

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Quantum Information Scientist

Quantum Information Scientists study the use of quantum mechanics to process and transmit information. This could include developing new quantum communication protocols, or creating new quantum cryptography algorithms. You will need a strong understanding of computer science, physics, and mathematics. This course will help build a foundation in quantum mechanics, which is essential for understanding the principles of quantum information science.

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Particle Physicist

Particle Physicists study the fundamental particles that make up matter and the forces that act between them. This could include developing new theories of physics, or using particle accelerators to search for new particles. You will need a strong understanding of physics and mathematics. This course will help build a foundation of quantum mechanics, which is essential for understanding the behavior of particles at the quantum level.

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Nanotechnologist

As a Nanotechnologist, you will be working on the development and application of materials and devices at the nanoscale. This could include developing new materials for electronics, or creating new drug delivery systems. You will need a strong understanding of chemistry, physics, and mathematics. This course will help build a foundation in quantum mechanics, which is essential for understanding the behavior of matter at the nanoscale.

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Theoretical Physicist

As a Theoretical Physicist, you will be developing new theories of physics. This could include developing new theories of quantum mechanics, or developing new theories of gravity. You will need a strong understanding of physics and mathematics. This course will help build a foundation of quantum mechanics, which is essential for developing new theories of physics.

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Laser Technician

Laser Technicians work on the installation, maintenance, and repair of laser equipment. This could be for a variety of industries, including manufacturing, healthcare, and research. You will need to have a strong understanding of optics and laser physics. This course will give you a strong foundational understanding of quantum mechanics, the principles lasers are based on, making you a more successful Laser Technician.

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Chemical Engineer

In today's day and age, we have come to rely on synthetic materials for nearly everything we use. A Chemical Engineer designs and manufactures these materials that we see all around us. You will be tasked with making sure that these materials are made to specifications, especially in terms of their physical properties. You may be working on anything from plastics and fuel to food and medicine. You will need advanced math, chemistry, and physics skills, which is why this course will prove very beneficial to your career. This course will help build a foundation of quantum mechanics, which is vital to your work, as you will be dealing with atoms and molecules on a daily basis. Also, it will help you with the advanced math and analysis you will need to perform in order to complete projects successfully.

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Optical Engineer

As an Optical Engineer, you will be designing and building optical systems. This could include anything from telescopes to lasers. You will need a strong understanding of optics and physics. This course will help build a foundation of quantum mechanics, which is essential for understanding the behavior of light at the quantum level.

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Photonics Engineer

As a Photonics Engineer, you will be working on the development and application of devices that use light. This could include developing new types of lasers, or creating new optical communication systems. You will need a strong understanding of optics and physics. This course will help build a foundation of quantum mechanics, which is essential for understanding the behavior of light at the quantum level.

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Research Scientist

As a Research Scientist, you will be conducting research in a variety of scientific fields. This could include developing new theories, or conducting experiments to test existing theories. You will need a strong understanding of the scientific method, and a strong foundation in mathematics and physics. This course will help build a strong foundation of quantum mechanics, which is becoming increasingly important in various scientific fields.

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Nuclear Engineer

Nuclear Engineers design, build, and operate nuclear power plants. You will need a strong understanding of physics, mathematics, and engineering. This course will help you understand the quantum effects that occur in nuclear reactions, which is essential for the safe operation of nuclear power plants. Also, this course may be useful if you work with lasers and other technologies based on quantum effects.

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Plasma Physicist

Plasma Physicists study the behavior of plasma, which is a state of matter that is made up of ionized gas. This could include developing new plasma technologies, or using plasma to study the behavior of stars. You will need a strong understanding of physics and mathematics. This course will help build a foundation of quantum mechanics, which is essential for understanding the behavior of plasma at the quantum level.

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Materials Scientist

As a Material Scientist, you will be researching properties of different types of materials and developing new materials with specific properties. This could be for a variety of industries, including aerospace, automotive, and electronics. You will need a strong understanding of chemistry, physics, and mathematics. This course may be useful for your work in developing new materials at the quantum level.

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Electrical Engineer

As an Electrical Engineer, you will be tasked with designing and building equipment and systems that use electricity. This could include anything from power plants to medical devices. You will need a strong understanding of physics, mathematics, and computer science. This course may be useful to you as you will work with quantum technologies like lasers and microprocessors.

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Medical Physicist

Medical Physicists use physics to develop and apply techniques for the diagnosis and treatment of disease. This could include developing new imaging techniques, or using radiation to treat cancer. You will need a strong understanding of physics, mathematics, and computer science. This course may be useful to you in understanding the quantum effects that occur in biological systems.

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