Licence 3

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Introduction to the synthesis of chemical elements in the Universe (Big Bang, stars)

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This optional course introduces the physical concepts used in Nanoscience and Nanotechnology. It will enable students to better understand the specific phenomena associated with the nanometric scale. It also includes an introduction to the 4 microscopes used to observe and measure at this scale: AFM, STM, MEB, MET...

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This optional course focuses on solving physics problems on the computer. It includes the use of the Python language for scientific programming, with particular emphasis on visualization and animation. It provides an introduction to the possibilities offered by numerical physics through various simulations (FDTD simulation of the propagation of a 1D electromagnetic wave, etc.).

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The course aims to provide an initial general introduction to physics as it relates to the biological sciences, and to put into context the use of modern physics concepts, methods and approaches to describe biological systems and their complexity, from the molecular to the cellular scale. This means understanding the central role that physics has played over the past century in learning about the organization and dynamics of complex living matter (from cells to populations of individuals). At the same time, we need to understand that biological systems represent a new opportunity for physicists to learn more about the complexity of living matter and its capacity for self-organization, regulation and control, with an eye also to new biomimetic applications.

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This UE is a continuation of the mathematics courses of L1 and the 1st^{semester of} L2. The mathematical tools necessary for the physicist in integration theory, functional transformations, complex variables and distributions will be presented.

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This UE represents the natural continuation of the UEs in classical Newtonian mechanics.

In the first part of the course, we take Classical Mechanics from the principle of least action to two new formulations: the Lagrangian formalism and the Hamiltonian formalism. We study the link between physical symmetries and conservation laws (E. Noether's theorem) and introduce Poisson brackets, which allow us to write the classical laws of temporal evolution of physical quantities in a form that already prefigures those of quantum mechanics.

In the second part of the course, starting from an examination of the experimental limits of classical mechanics, a new theory of mechanics is introduced: Quantum Mechanics. This is a theory that is conceptually completely different from previous classical theories, based on a description of physical phenomena in terms of probabilities and therefore no longer deterministic. It's a radical paradigm shift that has turned physics on its head over the last century, enabling a deeper understanding of physical nature, with fundamental and practical spin-offs that have radically changed the lives of mankind (atomic physics, chemistry, nuclear energy, transistors, LASERS, to name but a few). 

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This UE is a continuation of the electromagnetism and waves courses taken in L2.

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Practical work in various areas of physics.

Topics covered include the study of mechanical and electrical oscillating systems (simple and torsion pendulums, coupled pendulums, RLC circuits, inductively coupled circuits), acoustic waves, a few notions of wave optics (diffraction and interference), the use of electronic circuits to study components or electrical systems (diodes, LEDs and photodiodes, transmission lines) and the study of a few properties of matter (magnetism, photoelectric effect, Faraday effect).

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This module is an introduction to the concepts and methods of the statistical physics of equilibrium systems, with a bottom-up approach: start with examples and then give the general principles. It draws heavily on Harvey Gould and Jan Tobochnik's course. A historical introduction to the construction of Brownian motion theory forms the final chapter of the course.

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The course builds on the knowledge acquired in L1 and L2 to acquire the basics of special relativity (1/3 of the EU) and offer students a brief introduction to subatomic particle physics (2/3 of the EU). It will also provide an introduction to the description of the intimate structure of matter. After developing the tools of special relativity necessary for the rest of the course, we'll go into detail on both the study of atomic nuclei (nuclear physics) and that of "elementary" particles (subatomic physics proper). A first description of the standard model of particle physics and the basic concepts of nuclear physics will be given.

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Practical work in wave optics studies interference phenomena using Michelson and Fabry-Pérot interferometers as an application for high-resolution spectroscopy. (Michelson interferometer and Fabry-Pérot interferometer hands-on)

Interference phenomena are also recorded on holographic plates for the restitution and study of holograms (TP holography).

The polarization of light is studied and used to study birefringent materials (calcite, for example), liquid crystals, isotropic materials placed under stress (induced birefringence)... (TP birefringence)

The emission of electromagnetic waves by heated bodies is studied in blackbody practical exercises. The temperature of various hot bodies is determined using a pyrometer, spectroscopy and an infrared camera (for the human body, for example).

Lasers are also studied, their emission, longitudinal and transverse modes either on a "fixed" cavity, or on an open, adjustable cavity. (TP HeNe laser I and II)

The propagation speed of an intensity-modulated electromagnetic wave is measured by the phase shift of its modulation induced by its propagation. (TP speed of light)

Objects are analyzed using Fourier optics, which, after filtering, brings out or removes certain details. The study is also compared with digital Fourier filtering (TP strioscopie).

Finally, the property of certain substances subjected to a magnetic field to deviate the plane of polarization of the light passing through them is being studied in the Faraday effect TP.

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The aim of this course is to introduce the basics of physical hydrodynamics. The kinematic aspects are dealt with first: Euler and Lagrange formalism, analysis of the motion of an element of fluid volume, introduction of current and potential velocity functions, and applications to different types of flow. In the following section on fluid dynamics, we establish Euler's equation and Bernoulli's relation for the flow of perfect fluids, followed by the Navier-Stokes equation describing the flow of viscous Newtonian fluids. This will lead to the definition of the stress tensor and the Reynolds number, enabling us to deduce whether a flow is laminar or turbulent. The course concludes with an introduction to the mechanics of deformable solids : displacement field, expansion and deformation tensors.

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The tutored project is an experimental or digital simulation project carried out in groups of 3 students. It takes place in the practical workroom, on one of the many physics and chemistry topics on offer. It confronts students with the project approach, and mobilizes their creativity, initiative, autonomy and experimental rigor. The project culminates in a report and oral presentation, subject to peer and jury assessment.

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This module covers selected methods of numerical physics with applications relevant to the Fundamental Physics pathway. After a review of programming with Python 3, numerical algorithms for solving nonlinear equations, ordinary differential equations and systems of linear equations will be studied. A major part of the module will concern numerical linear algebra and its applications in physics and numerical analysis. Finally, there will be an introduction to formal calculus systems.

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This course builds on the basic concepts acquired in Quantum Mechanics in Semester 5. The course is structured around the following main themes: extension of the wave mechanics formalism, angular momentum theory, hydrogen atom, perturbations, introduction to relativistic quantum mechanics.

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Practical work in various areas of physics.

Topics covered include the study of mechanical oscillating systems (simple pendulum, torsion pendulum, coupled pendulums), acoustic waves, a few notions of wave optics (diffraction and interference), the use of electronic circuits to study electrical components or systems (diodes, LEDs and photodiodes, transmission line) and the study of a few properties of matter (magnetism, photoelectric effect, Faraday effect).

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Introduction to the synthesis of chemical elements in the Universe (Big Bang, stars)

See full page

This optional course introduces the physical concepts used in Nanoscience and Nanotechnology. It will enable students to better understand the specific phenomena associated with the nanometric scale. It also includes an introduction to the 4 microscopes used to observe and measure at this scale: AFM, STM, MEB, MET...

See full page

This optional course focuses on solving physics problems on the computer. It includes the use of the Python language for scientific programming, with particular emphasis on visualization and animation. It provides an introduction to the possibilities offered by numerical physics through various simulations (FDTD simulation of the propagation of a 1D electromagnetic wave, etc.).

See full page

The course aims to provide an initial general introduction to physics as it relates to the biological sciences, and to put into context the use of modern physics concepts, methods and approaches to describe biological systems and their complexity, from the molecular to the cellular scale. This means understanding the central role that physics has played over the past century in learning about the organization and dynamics of complex living matter (from cells to populations of individuals). At the same time, we need to understand that biological systems represent a new opportunity for physicists to learn more about the complexity of living matter and its capacity for self-organization, regulation and control, with an eye also to new biomimetic applications.

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Learn about analog and digital electronics.

Analog teaching is based on the study and application of the main electronic components: diodes, transistors and operational amplifiers.

For the numerical part, the basics of sequential logic will be covered.

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At the start of this course, we will review the concepts of light rays and the approximation conditions of geometrical optics, as well as the important concepts of wave physics for physical optics.

Then, starting from the scalar approximation of light waves, a special case of electromagnetic waves, we describe light sources, 2-wave and N-wave interference phenomena and diffraction in the Fraunhofer approximation.

We'll go on to study a number of widely-used physical systems, focusing on their resolving power and applications: microscope, telescope, Michelson interferometer, grating spectrometer, Fabry-Pérot interferometer.

Finally, we'll look at the concepts of spatial coherence and temporal coherence of light bursts, and how they are used (stellar interferometry, speckle, etc.).

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This course is a simplified introduction to quantum physics.
It begins with an historical overview of the beginnings of quantum mechanics: atomic emission line spectra, black-body radiation (the logic of this name will be explained), the photoelectric effect, etc.
A simplified presentation of Fourier transforms will enable us to understand the link between spectral line width and time evolution,
and, further on, to understand Heisenberg's inequalities.
An important part of the course will be devoted to matter waves, through the Schrödinger equation, in very simple special cases.
Finally, we'll conclude with a few aspects of magnetism (necessarily quantum).

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Statistical physics is one of the fundamental branches of modern physics, whose probabilistic approach establishes relationships between the microscopic and the macroscopic. It deals with the evolution of systems with very large numbers of particles (atoms, molecules, photons, etc.) and links macroscopic quantities such as pressure, temperature, etc. characterizing their state at thermodynamic equilibrium to quantities defining the microscopic state of their constituents. This introductory course in statistical physics will cover the microcanonical and canonical sets, and relate the partition function to thermodynamic quantities such as mean energy, pressure, temperature and entropy. These results will be illustrated on perfect gases and on a few simple quantum systems.     

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This UE is made up of two blocks of 18 hours each (9h CM+ 9h TD).

For the first "acoustics" block, after establishing the equation for the propagation of mechanical vibrations in an infinite medium, plane-wave solutions will be presented. Emphasis will then be placed on the notion of scalar potential. Spherical wave solutions will be presented. A large part will be devoted to the notion of acoustic impedance. Energy aspects will also be discussed. Various applications (particularly ultrasonic) will be covered.

The second "thermal" block of the course studies heat transport properties in solids and fluids under stationary (time-independent) conditions. We first define diffusive and convective heat transfer regimes, and introduce the Fourier equation linking heat flow to temperature variation via thermal conductivity or the conducto-convective coefficient. We then establish the heat propagation equation, which we apply to the simple cases of walls and pipes. We then review the main laws describing heat transfer by radiation (Planck's law, Stefan-Boltzmann's law) and study the case of radiative flux between two bodies under total influence. All this knowledge will be used to carry out heat balances for homogeneous or composite walls, building models, bars and fins. We'll also look at heat exchangers.

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This UE includes a refresher and a deepening of programming techniques as well as an introduction to numerical physics. It begins with a review of procedural programming using the Python 3 language. We will then introduce the use of numerical methods relevant to the simulation and solution of physical problems.

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This UE is a continuation of the point dynamics and rigid solid mechanics taught in L1 and L2. The aim here is to provide elements of the mechanics of deformable continuous media, essentially in the limit of small deformations, linear elasticity, viscoelasticity and viscosity. Emphasis is placed on simple cases and common applications.

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The tutored project is an experimental or digital simulation project carried out in groups of 3 students. It takes place in the practical workroom, on one of the many physics and chemistry topics on offer. It confronts students with the project approach, and mobilizes their creativity, initiative, autonomy and experimental rigor. The project culminates in a report and oral presentation, subject to peer and jury assessment.

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This course is divided into two parts. The first part focuses on the Dirac formalism in quantum mechanics, with illustrations in the case of the 1D harmonic oscillator and angular momentum, in particular for spin. The second part is an introduction to the use of quantum mechanics in solid state physics, through its application to semiconductors.

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Classification of solids. Crystalline structures. Energy bands. Metals. Semiconductors. Insulators. Electrical, dielectric and magnetic properties.

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Study of the basic principles of nucleus physics with a view to concrete everyday applications. The aim of this course is to provide a basic understanding of the physics of the nucleus, followed by a presentation of the applications of radioactivity and nuclear energy in industry (physics of nuclear reactors, fuels), medicine (nuclear imaging) and radiation protection (measuring instruments, units, etc.).

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Practical work and application of analog and digital electronics in connection with UE HLPH507.

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Introduction to the synthesis of chemical elements in the Universe (Big Bang, stars)

See full page

This optional course introduces the physical concepts used in Nanoscience and Nanotechnology. It will enable students to better understand the specific phenomena associated with the nanometric scale. It also includes an introduction to the 4 microscopes used to observe and measure at this scale: AFM, STM, MEB, MET...

See full page

This optional course focuses on solving physics problems on the computer. It includes the use of the Python language for scientific programming, with particular emphasis on visualization and animation. It provides an introduction to the possibilities offered by numerical physics through various simulations (FDTD simulation of the propagation of a 1D electromagnetic wave, etc.).

See full page

The course aims to provide an initial general introduction to physics as it relates to the biological sciences, and to put into context the use of modern physics concepts, methods and approaches to describe biological systems and their complexity, from the molecular to the cellular scale. This means understanding the central role that physics has played over the past century in learning about the organization and dynamics of complex living matter (from cells to populations of individuals). At the same time, we need to understand that biological systems represent a new opportunity for physicists to learn more about the complexity of living matter and its capacity for self-organization, regulation and control, with an eye also to new biomimetic applications.

See full page

See full page

This UE represents the natural continuation of the UEs in classical Newtonian mechanics.

In the first part of the course, we take Classical Mechanics from the principle of least action to two new formulations: the Lagrangian formalism and the Hamiltonian formalism. We study the link between physical symmetries and conservation laws (E. Noether's theorem) and introduce Poisson brackets, which allow us to write the classical laws of temporal evolution of physical quantities in a form that already prefigures those of quantum mechanics.

In the second part of the course, starting from an examination of the experimental limits of classical mechanics, a new theory of mechanics is introduced: Quantum Mechanics. This is a theory that is conceptually completely different from previous classical theories, based on a description of physical phenomena in terms of probabilities and therefore no longer deterministic. It's a radical paradigm shift that has turned physics on its head over the last century, enabling a deeper understanding of physical nature, with fundamental and practical spin-offs that have radically changed the lives of mankind (atomic physics, chemistry, nuclear energy, transistors, LASERS, to name but a few). 

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In the first part: deepen the basic notions of differential calculus seen in L2.

In the second part: introduce the qualitative study of differential equations.

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This UE is a continuation of the electromagnetism and waves courses taken in L2.

See full page

Practical work in various areas of physics.

Topics covered include the study of mechanical and electrical oscillating systems (simple and torsion pendulums, coupled pendulums, RLC circuits, inductively coupled circuits), acoustic waves, a few notions of wave optics (diffraction and interference), the use of electronic circuits to study components or electrical systems (diodes, LEDs and photodiodes, transmission lines) and the study of a few properties of matter (magnetism, photoelectric effect, Faraday effect).

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The aim of this first Fluid Mechanics module is to provide a basic understanding of the behavior of industrial fluids (air, water, hydraulic fluids), with a view to dimensioning simple systems involving static or dynamic fluids (flow rates, pressure, velocity, pressure drops, etc.). Emphasis is placed on the study and design of hydraulic installations.

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This module is an introduction to the concepts and methods of the statistical physics of equilibrium systems, with a bottom-up approach: start with examples and then give the general principles. It draws heavily on Harvey Gould and Jan Tobochnik's course. A historical introduction to the construction of Brownian motion theory forms the final chapter of the course.

See full page

The course builds on the knowledge acquired in L1 and L2 to acquire the basics of special relativity (1/3 of the EU) and offer students a brief introduction to subatomic particle physics (2/3 of the EU). It will also provide an introduction to the description of the intimate structure of matter. After developing the tools of special relativity necessary for the rest of the course, we'll go into detail on both the study of atomic nuclei (nuclear physics) and that of "elementary" particles (subatomic physics proper). A first description of the standard model of particle physics and the basic concepts of nuclear physics will be given.

See full page

Practical work in wave optics studies interference phenomena using Michelson and Fabry-Pérot interferometers as an application for high-resolution spectroscopy. (Michelson interferometer and Fabry-Pérot interferometer hands-on)

Interference phenomena are also recorded on holographic plates for the restitution and study of holograms (TP holography).

The polarization of light is studied and used to study birefringent materials (calcite, for example), liquid crystals, isotropic materials placed under stress (induced birefringence)... (TP birefringence)

The emission of electromagnetic waves by heated bodies is studied in blackbody practical exercises. The temperature of various hot bodies is determined using a pyrometer, spectroscopy and an infrared camera (for the human body, for example).

Lasers are also studied, their emission, longitudinal and transverse modes either on a "fixed" cavity, or on an open, adjustable cavity. (TP HeNe laser I and II)

The propagation speed of an intensity-modulated electromagnetic wave is measured by the phase shift of its modulation induced by its propagation. (TP speed of light)

Objects are analyzed using Fourier optics, which, after filtering, brings out or removes certain details. The study is also compared with digital Fourier filtering (TP strioscopie).

Finally, the property of certain substances subjected to a magnetic field to deviate the plane of polarization of the light passing through them is being studied in the Faraday effect TP.

See full page

The aim of this course is to introduce the basics of physical hydrodynamics. The kinematic aspects are dealt with first: Euler and Lagrange formalism, analysis of the motion of an element of fluid volume, introduction of current and potential velocity functions, and applications to different types of flow. In the following section on fluid dynamics, we establish Euler's equation and Bernoulli's relation for the flow of perfect fluids, followed by the Navier-Stokes equation describing the flow of viscous Newtonian fluids. This will lead to the definition of the stress tensor and the Reynolds number, enabling us to deduce whether a flow is laminar or turbulent. The course concludes with an introduction to the mechanics of deformable solids : displacement field, expansion and deformation tensors.

See full page

The tutored project is an experimental or digital simulation project carried out in groups of 3 students. It takes place in the practical workroom, on one of the many physics and chemistry topics on offer. It confronts students with the project approach, and mobilizes their creativity, initiative, autonomy and experimental rigor. The project culminates in a report and oral presentation, subject to peer and jury assessment.

See full page

This module covers selected methods of numerical physics with applications relevant to the Fundamental Physics pathway. After a review of programming with Python 3, numerical algorithms for solving nonlinear equations, ordinary differential equations and systems of linear equations will be studied. A major part of the module will concern numerical linear algebra and its applications in physics and numerical analysis. Finally, there will be an introduction to formal calculus systems.

See full page

This course builds on the basic concepts acquired in Quantum Mechanics in Semester 5. The course is structured around the following main themes: extension of the wave mechanics formalism, angular momentum theory, hydrogen atom, perturbations, introduction to relativistic quantum mechanics.

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Introduce the basic tools of complex analysis.

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