This advanced quantum mechanics course covers both foundational principles and more applied modern topics. The journey begins with a review of core principles and the pivotal role of symmetries, before extending to higher-dimensional systems, angular momentum, and spin. Moving into composite quantum systems, the curriculum introduces tensor products, the addition of angular momenta, and entanglement, built around a discussion of the EPR paradox and its implications for quantum cryptography. From there, students explore approximation methods (such as perturbation theory), identical particles, time evolution, and the mechanics of charged particles in magnetic fields, including Landau levels and the rotating-wave approximation. The course concludes with the Feynman path integral formulation. Each week features a lecture paired with an in-class exercise session grounded in physical applications like carbon nanotubes, nuclear magnetic resonance, and the fine structure of sodium.
In Advanced Lab III, students have the opportunity to apply the physics knowledge they have acquired over the course of 6 lab sessions of 4 hours each. In PHY_3F003_EP, the students will discover a more autonomous style of experimentation. The lab sessions will be centered on modern physics and are expected to address the following subjects: quantum physics (scanning tunneling microscope, superconducting quantum interference device), condensed matter physics (X ray diffraction and crystallography), modern optics (lasers) as well as solid and fluid mechanics (mechanics of deformable bodies).
This course introduces the fundamental quest to understand the ultimate constituents of matter and the laws that govern their interactions, from the subatomic scale to the vastness of the Universe.
The quest to identify the ultimate constituents of matter has revealed a nested structure spanning many orders of magnitude: atoms contain electrons and nuclei; nuclei are made of nucleons, themselves composed of quarks and gluons. Today, particle physics focuses on the fundamental laws governing these constituents and their interactions, with key questions such as how particles acquire mass, illuminated by the 2012 discovery of the Higgs boson at the LHC, notably by experiments like CMS.
At the same time, the infinitely small is deeply connected to the infinitely large: studies of neutrinos and astroparticles, including the highest-energy cosmic rays whose origins may lie in extreme astrophysical environments such as black hole accretion disks, link particle physics to cosmology and the physics of the early Universe. This field also relies on cutting-edge research and development in detectors and instrumentation, driving innovation while pushing the frontiers of our understanding of the cosmos.
Recommended previous courses: PHY102, PHY107, PHY201, PHY204, PHY205, PHY206
Condensed matter physics deals with the description of the physical properties of matter when the interaction between its constituents are very strong. This is typically the case for materials and devices. It covers a very large field of knowledge that encompasses electric, thermal, chemical, magnetic, and mechanical properties, and all the combinations of these properties, in solids.
From the technological point of view, condensed matter physics have brought some major discoveries and new developments: electronic devices, sensors, actuators, transductors, power generation devices, energy storage, to name but a few.
This domain of physics is based on two different and complementary approaches. A first approach starts from the quantum microscopic constituents and describes statistically the macroscopic consequences. The second is a phenomenological macroscopic description based on general principles of thermodynamics and symmetries.
Thermodynamics and statistical physics are two pivotal frame theories, with uncountable applications in many fields. Thermodynamics offers a conceptual framework that is both elegant and remarkably fruitful for describing the physics of a wide variety of macroscopic systems. It makes it possible to understand, describe, and predict the physics of systems as diverse as molecular gases, fluids, magnetic materials, as well as astrophysical objects, such as stars, galaxies or even the entire Universe. Statistical physics, on the other hand, permits to justify the axioms of thermodynamics and, more importantly, go significantly beyond, bridging the gap between the microscopic and macroscopic scales. It played a major role in the revolution of physics in the 20th century, paving the way for major advances. In the first place, it makes it possible to understand how quantum effects show up at the macroscopic scale, for instance in condensed-matter physics or in astrophysics.
The aim of this course is to offer an introduction to thermodynamics and statistical physics, and discuss a number of applications in a variety of contexts, from classical to quantum.
