Prerequisite: PHY205

As its name suggests, this course is a sequel to PHY205 “Introduction to Quantum Physics”. It will expand our view on three-dimensional quantum mechanical problems, by applying the formalism to the description of atoms and particles in a magnetic field. This includes also a deeper analysis of angular momentum, and its relation to rotational symmetry. We will discover approximation techniques for time-independent and time-dependent phenomena, and apply them to the detailed description of the hydrogen atom. The quantum-mechanical description of scattering will be introduced. Furthermore, we will study the notion of entanglement which is fundamental to quantum cryptography and quantum computing. The description of identical particles in quantum mechanics will build the bridge to the Pauli exclusion principle and the spin-statistics connection.

The following subjects are expected to be treated:

❯ The addition of angular momenta
❯ The notion of spin and magnetic resonance
❯ Approximation methods and time independent perturbation theory
❯ Entangled states and the EPR paradox
❯ Particles in a magnetic field, Landau levels
❯ Identical particles and the spin-statistics connection
❯ Time-evolution and time-dependent perturbation theory

Recommended previous courses: PHY203, PHY207

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 PHY303, 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 (e.g. Nuclear magnetic resonance), condensed matter physics (e.g. crystallography), modern optics (e.g. lasers) as well as solid and fluid mechanics (e.g. mechanics of deformable bodies). Upon completion of this course, students will have acquired advanced experimental skills allowing them to set up, carry out and to critically analyze experiments in physics.

Upon completion of this course, students will have acquired advanced experimental skills allowing them to set up, carry out and to critically analyze experiments in physics.

Prerequisites: PHY204, PHY205
Recommended previous courses: PHY106, PHY301

The quest for finding the ultimate constituents of matter has revealed that matter has a nested structure at scales that differ by many orders of magnitudes: atoms contain electrons and nuclei; nuclei are made up of nucleons, which in turn are composed of quarks and gluons. Nowadays, particle physicists are more concerned with the fundamental laws that govern the interactions of elementary particles. The most emblematic question is “how do particles acquire mass”; and the discovery of the Higgs boson in 2012 is an important clue that we are on the right path to answering this question. The infinitely small is also intimately linked to the infinitely large: to cite just one example, the most energetic particles detected to date, called cosmic rays, come from processes whose origin remains a mystery, probably created in the heart of accretion disks surrounding black holes, located at the center of active galaxies.

This course will give a pedestrian introduction to the subatomic physics, with 4 courses dedicated to the special relativity, 5 courses about the nuclear and high energy physics and 4 courses about high energy astrophysics. All courses will be illustrated in a balanced theoretical underpinning, experimental activities and technological aspects of subatomic physics. The bases for this course will be PHY205 (introductory quantum physics) and PHY204 (theoretical electrodynamics).

 

In the special relativity section, the following subjects will be treated: Lorentz transformations, spacetime diagrams, covariant formalism, 4-vectors including the energy-momentum vector, illustrated by several examples such as the famous twin paradox.

The nuclear and subatomic part of the course will provide the big picture of the structure of matter with the great discoveries. The nuclear models (droplet model) and the nuclear binding energy will be discussed. The Standard Model components and interactions will be presented, through the particle evolution equations and an introduction to the Feynman’s diagrams including the different conservation laws of the Standard Model. This section will end with a course dedicated to the particle accelerators/colliders and detectors and a discussion about the latest measurements arguing for a theory beyond the Standard Model.

In the last 4 courses, we will dive into the high energy astrophysics, where we will review nuclear and particle physics in various astrophysical environments. We will start with an introduction with a first course about stellar mass compact objects, from white dwarfs to black holes; and a second course dedicated to the environments of supermassive black holes, at the heart of active galactic nuclei. The 2 last courses will cover the high energy processes in astrophysics with a first lecture dedicated to the accretion and ejection phenomena, super-luminal jets, thermal and non-thermal processes; while the second lecture will detail synchrotron radiation, Inverse Compton, leptonic and hadronic interactions, diffusion and collision.

 

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.