Physical and Chemical Profile

Statistical physics is one of the fundamental branches of modern physics; through its probabilistic approach, it establishes relationships between the microscopic and the macroscopic. It deals with the behavior of systems containing a very large number of particles (atoms, molecules, photons, etc.) and links macroscopic quantities—such as pressure, temperature, etc.—that characterize their state of thermodynamic equilibrium to quantities that define the microscopic state of their constituents. This course unit, an introduction to statistical physics, will cover the microcanonical and canonical ensembles and establish the connection between the partition function and thermodynamic quantities such as average energy, pressure, temperature, and entropy. These results will be illustrated using ideal gases and a few simple quantum systems.     

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This course is a simplified introduction to quantum physics.
We will begin by providing a historical overview of the early days of quantum mechanics: atomic emission spectra, blackbody radiation (we will explore the logic behind this term), the photoelectric effect, etc.
A simplified introduction to Fourier transforms will help us understand the relationship between spectral line width and time evolution at first,
and later on, help us understand Heisenberg’s uncertainty principle.
A significant portion of the course will be devoted to matter waves, through the Schrödinger equation, in very simple special cases.
Finally, we will conclude with a few aspects of magnetism (which is, of course, quantum in nature).

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The first part of the module will introduce metals and alloys through the lens of crystallography (from the “ideal” crystalline solid to defects and solid solutions), followed by a second part devoted to their characterization by X-ray diffraction, and the final part will address their synthesis using their solid-liquid binary phase diagram (description and construction) and the various solid-state transformations.

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Thermodynamics: Microscopic and Macroscopic Aspects

Thermodynamics is the tool of choice for studying matter on a macroscopic scale. In particular, when it comes to chemical reactions, it allows us to predict the direction in which they proceed and their equilibrium state. In the early years of the bachelor’s program, the focus is on describing the principles of thermodynamics and their direct application to chemistry in the case of simple, single-phase equilibrium reactions or reactions between homogeneous phases. This course will expand on this knowledge in two directions.

First, we will generalize this macroscopic thermodynamic descriptive framework to more complex systems, such as interfacial systems where surface tension plays a role, or non-uniform phases where the composition is not the same everywhere due to an external field. We will also study phase transitions and equilibrium displacements.

Next, we will examine the connection to the microscopic world, where matter is described at the atomic scale. We will show that the evolution predicted by thermodynamics is statistical in nature, with the equilibrium state corresponding to the most probable macroscopic state given the constraints imposed on the system. This will allow us to deduce the macroscopic thermodynamic properties of a physicochemical system from its microscopic description.

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At the beginning of this course unit, we will review, on the one hand, the concepts of light rays and the conditions for the approximation of geometric optics and, on the other hand, the concepts in wave physics that are important for physical optics.

Then, starting with the scalar approximation of light waves—a special case of electromagnetic waves—we will describe light sources, interference phenomena involving two waves and N waves, and then diffraction in the Fraunhofer approximation.

We will continue by studying various widely used physical systems, focusing on their resolving power and applications: the microscope, the telescope, the Michelson interferometer, the diffraction grating spectrometer, and the Fabry-Pérot interferometer.

Finally, we will conclude with the concepts of spatial and temporal coherence of light sources and their applications (stellar interferometry, speckle, etc.)

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