An introduction to the fundamentals of mechanics. Vector analysis and its application to the analysis of the motion of particles and rigid bodies. Newton's three laws of motion. The kinematics and dynamics of particle motion along straight and curved paths. Work, energy, impulse and momentum of particles and rigid bodies. An introduction to the rotation of a rigid body about a fixed axis, moments of inertia, angular momentum. Simple Harmonic Motion. 

This course provides the student hands-on experience with concepts covered in PHYS 1051.

This course provides the student hands-on experience with concepts covered in PHYS 1052. 

This course aims to investigate the two way interaction between society and physics. The ideas of physics have percolated into the collective consciousness both as scientific knowledge and as cultural reference points and various new technologies can be identified as originating in physics research. However, physics also has to deal with how it is perceived as a discipline and how physicists are perceived as trustworthy authorities. Open to students in all faculties. No mathematics beyond basic high school algebra and geometry is needed. Content. Introduction to the philosophy of science and the scientific method, introduction to the major scientific ideas that have shaped our society and the world. 

Role within programme and connections to other courses. This course is an important - and big! - first step away from the tremendously simplified problems that we have dealt with both in introductory university physics and in high school. We introduce the integration of greater mathematical sophistication in the treatment of physical situations, showing that comfort with a variety of mathematical techniques will allow us to study a greater range of - and more interesting - problems. Furthermore, this course serves to show that familiarity with the powerful Newtonian toolchest, which we have been using since high school, allows us to approach complicated, realistic situations with confidence. The inclusion of special relativity challenges us to think beyond the familiar. Content. Special relativity (including elements related to the development of the theory), advanced Newtonian kinematics and dynamics (translational and rotational), conservation principles.

Role within programme and connections to other courses. This course introduces an entirely new approach to mechanics, one that is more elegant and more powerful but less intuitive than the Newtonian approach to which we have been exposed thus far. This is the last compulsory mechanics course and, therefore, includes the classical mechanics background for the quantum mechanics stream. Some computational exercises are included (e.g. the use of numerical differential equation solvers). Content. Mechanics in non-inertial reference frames, calculus of variations, Lagrangian mechanics, two-body, central force problems (orbital motion), rotational motion of rigid bodies, an introduction to Hamiltonian mechanics. 

Role within programme and connections to other courses. Understanding circuits and basic electronics is essential for any physicist who will develop or simply use measuring devices. This course moves beyond the simple DC circuits involving resistors and capacitors seen in introductory physics. It introduces the basic elements of the many electronic devices which we use every day, then shows how to combine these elements when designing simple circuits. This topic is particularly well-suited to hands-on learning. The course is experiential in design with more time devoted to manipulations than to lecture. Through the experimental work involved in learning about basic electronics, we are introduced to and become comfortable with essential measurement apparati (multimeters, oscilloscopes, etc). The understanding of basic electronics and measuring devices gained from this course will serve to enhance all future laboratory work: the equipment will not distract us from the physical phenomena which we are studying and we will understand how to best use the equipment and appreciate its limitations. This course also introduces some computational techniques for circuit analysis e.g. in the solution of simultaneous linear equations. Content. AC circuits, operational amplifiers, diodes and other pertinent topics.

Role within programme and connections to other courses. This course helps us to acquire skills needed to do research. These include two different aspects: (1) how to deal with experimental limitations (2) how to read and write scientific documents. The skills acquired in this course are subsequently applied in other courses. In all future experimental work, we will treat experimental limitations properly and fully. In all future courses involving reports, written work will meet or exceed the standards established in the Research Skills course. The title of this course emphasises the fact that the programme does more than fill us with physics facts. This is also an opportunity to review other skills, which are developed by the programme (problem solving strategies, approximation, presentation skills, index/abstract searching, etc.). All of these skills are generally applicable in physics & beyond. Content. Uncertainty analysis, Data processing and analysis, Reading and understanding technical literature, Technical writing. 

This course includes some experimental work that supports the lecture material.
Role within programme and connections to other courses. This course furnishes us with classical thermodynamics and a little about properties of materials. We have heard that “energy is conserved” and even have an appreciation of how important this principle is, but in first year mechanics energy is often apparently “lost” when friction does work. Here, at last , we introduce a complete formulation for energy conservation, comparing the work defined in first year with heat as a means of energy transfer. We discuss transformations of energy in a variety of processes, then go on to explain that not all of the energy is available for doing mechanical work. The theoretical framework of classical thermodynamics is beautifully self-contained, but this course also emphasises the link between the microscopic world of the kinetic theory (drawing on Newtonian mechanics as it does so) and the macroscopic world of the everyday, in preparation for the statistical thermodynamics to follow.
Content. Gases (ideal and real) and pressure, phases and phase diagrams, the state of a system, what is energy?, heat and work, first, second and third laws of thermodynamics, entropy, enthalpy and free energies, heat engines, refrigerators, heat pumps and efficiency, phase transitions, introductory kinetic theory.

This course includes some experimental work that supports the lecture material.
Role within programme and connections to other courses. This course lays the necessary foundations for thinking about phenomena on very small spatial scales. This course calls on many concepts learned in introductory physics: position, momentum, energy, angular momentum, vibrations, waves. It casts many of them in a new light, at times requiring modification of the classical definition of these quantities. Quantum Physics serves as the foundation for the more in–depth learning of the tools of quantum mechanics presented in the Quantum Mechanics trio of courses and the courses which follow from these. In addition, Quantum Physics is essential background for the study of astrophysics and atmospheric physics.
Content. Particle properties of waves: blackbody radiation, photoelectric effect, Compton effect; wave properties of particles: de Broglie waves, Davisson-Germer experiment, the uncertainty principle; old atomic theory: atomic spectra, Rutherford’s model, Bohr’s model, spontaneous and stimulated transitions, lasers; quantum mechanics: the Schrodinger equation, mathematical tools; quantum mechanical examples: square wells and barriers, quantum tunnelling and its applications; quantum theory of atoms.

This course includes some experimental work that supports the lecture material. Role within programme and connections to other courses. Oscillations and waves are key elements to understanding many subfields and applications of physics. Acoustics, optics and electromagnetism (telecommunications) are obvious examples, but waves are also essential to understanding quantum mechanics (the Schrödinger formalism), some atmospheric phenomena, seismic phenomena and fluid mechanics. Content. Oscillatory motion, waves applications to optics and acoustics.

Role within programme and connections to other courses. This course is meant to help us develop the skills needed to communicate with non-specialists concerning physics. Given that most physics research is ultimately paid for by the public, it behooves physicists to communicate effectively with those who are funding their work, for the benefit of both parties. The goal of such communication is two-fold: (1) to insure that the general public is physics literate and therefore able to enter into a discourse about the science, and (2) to insure that the next generation of university students is exposed to physics in such a way that they can make an informed choice about whether or not their academic and career paths should include physics.
Content. Topics may include: science journalism, science museums and exhibits, outreach to schools and other groups, physics education and physics education research.

Role within programme and connections to other courses. With the population of the planet increasing and the natural resources decreasing, it is more important than ever to understand the manner in which those resources can and are being used as well as the environmental impacts of those uses. In addition, part of understanding those impacts is understanding how measurements of impacts are made. By focussing on applications of physics to environmental matters, this course contributes to the synthesis of concepts and models learned in other courses. Content. The main focus of the course is on matters related to energy, its production, extraction, distribution and use. Topics include hydroelectricity, solar power, nuclear power, fossil fuels, etc. 

Role within programme and connections to other courses. This course will be our first major foray into the formalism of electromagnetic theory. A thorough examination of the nature of vector fields and the forces they cause, and scalar fields along with their relationship to energy, will form a connection to earlier discussions started in Mechanics I. The tools studied previously in Intermediate Calculus (vector operations and calculus) and Methods of Theoretical Physics (particularly special functions like Legendre polynomials and spherical harmonics, delta functions, and tensor analysis) will play a significant role here. Content. Interactions between point charges, the nature and calculation of the electric and magnetic fields, the distribution of electric and magnetic fields in space (flux, Gauss’ law, Ampère’s law), reactions of charges and dipoles to applied fields, electrostatic scalar potential and magnetic vector potential, elementary gauge theory, energy storage in static electric and magnetic fields, elementary treatment of fields in materials, fields across boundaries, time dependence of electromagnetic fields, displacement current, the final form of Maxwell’s equations, electromagnetic waves. 

Role within programme and connections to other courses. In the course of an undergraduate physics programme we employ a variety of theoretical techniques. This course exposes us to theoretical ideas that are widely applicable in electromagnetism, quantum mechanics, classical mechanics and relativity. Special emphasis will be placed on demonstrating the general nature of the topics considered. Content. Non-orthogonal, non-normalised bases, tensors, special functions (general solutions to second order differential equations) and expansions in special functions, integral transforms (Fourier, z-transform, Laplace transform).

Role within programme and connections to other courses. Various courses contain experiments that are directly related to the material addressed in the lectures, however, in the interest of promoting an understanding of connectivities (avoiding compartmentalisation) and refining research skills, this synthesis course will contain a variety of experiments, many of which integrate concepts learned in diverse courses. Content. The experiments include topics in mechanics, electromagnetism, quantum physics, thermal physics and optics.

Role within programme and connections to other courses. Every physics honours student is required to complete one independent study course, to allow the development of critical reading and thinking skills. This course shall be taken no sooner than the beginning of his/her third year and no later than the penultimate term of his/her degree (i.e. the student must know a sufficient amount of physics to allow for a challenging independent study course, and the student should complete this course before working on his/her Advanced Research Project so that the skills developed during the independent study course are of use during the thesis project).
Content. The student will choose among the list of topics for which supervision has been offered or can choose some other topic of interest if (s)he can convince a faculty member to supervise the course.

Role within programme and connections to other courses. This course builds from the bottom up (molecules → continuous phases) what Thermal Physics describes from the top down (macroscopic properties → kinetic theory). We reinforce the idea (from Quantum Physics and Quantum Mechanics I) that our macroscopic observations can be based on underlying probabilities, rather than strict determinism. Content. The ensemble basis for basic statistics, equilibrium between interacting systems, the Laws of Thermodynamics (from a microscopic standpoint), classical and quantum statistical distributions, applications of Maxwell-Boltzmann statistics, kinetic theory of gases revisited, applications of quantum statistics.

Role within programme and connections to other courses. The need for and qualities of quantum mechanics have been clearly established in Quantum Physics. This course begins to put quantum mechanics on a formal footing. The approach in QM I is expected to include both wave and matrix techniques.
Content. Mathematical structure of quantum mechanics, Hilbert space, operator algebra; postulates of quantum mechanics, symmetries and conservations; quantum dynamics; general theory of angular momentum, coupling of angular momenta, irreducible tensor operators, Wigner-Eckart theorem; analytical solution of the hydrogen atom; identical particles: spin and statistics, the Pauli exclusion principle and many electron atoms.

Role within Program and connections to other courses: Optics is of immense practical importance. Optical phenomena provide a direct connection between the macroscopic world and the microphysics behind it. Includes application of theoretical concepts introduced in electromagnetic theory and quantum mechanics. Serves as the foundation for later courses in the Optical Engineering stream of the Engineering Physics program. Content: Models of microscopic behaviour relevant to understanding optical phenomena: geometric optics, physical optics, electromagnetic theory, quantum mechanics. Topics may include radiometry, imaging, colour and spectra, polarization, coherence, interference, diffraction, the scattering/wavelet model, and the formalisms explaining them. Lectures may also include demonstrations and experiments to support the material.  

Role within programme and connections to other courses. For an undergraduate student, atomic and molecular physics is one of the most fundamental applications of quantum mechanics in the curriculum. The course provides a firm grounding in quantum angular momentum theory, including spin and angular momentum coupling, and makes extensive use of the matrix approach to quantum physics calculations. The course is linked to all courses in the quantum mechanics stream, and to optics.
Content. Quantum angular momentum concepts, including orbital angular momentum, spin, and angular momentum coupling, the hydrogen atom, including spin-orbit and hyperfine interactions, methods and approaches to multi-electron atoms, topics in molecular physics, including development of the Hamiltonian, the Born-Oppenheimer approximation, and the structure of molecular spectra. Usually offered on rotation with Subatomic Physics and Solid State Physics.

Role within programme and connections to other courses. The study of nuclear and particle physics draws mainly on quantum physics but, due to the semi-empirical nature of many of the nuclear models used, it also draws heavily on basic electromagnetism and other branches of physics. An understanding of nuclear physics is essential for work related to radiation therapy, in the nuclear energy sector, and in some branches of astrophysics. As for particle physics, as well as being a field in its own right, it has become inextricably linked to research in cosmology.
Content. Some overlap of topics with environmental physics and medical physics is to be expected, but the approach and depth will differ greatly. Exact content will be at the instructor’s discretion allowing the course to focus sometimes more on applications of nuclear physics, sometimes more on particle physics, etc. Usually offered on rotation with Atomic & Molecular Physics and Solid State Physics.

Role within programme and connections to other courses. Atmospheric events and processes have an impact on and are impacted by human activity, making atmospheric physics a topic of great societal relevance. The study of the atmosphere requires consideration of a wide range of spatial scales — from radiation transfer at the atomic level to phenomena on the global level — and a wide range of time scales — from seconds to centuries. Making headway requires an understanding of what processes can and cannot be ignored depending on the scales under consideration. In addition to providing an introduction to the field of atmospheric physics, this course contributes toward the overall goal of the physics programme by calling on us to combine knowledge from a variety of subfields of physics. Knowledge acquired in thermal physics, in mechanics and in quantum physics (blackbody radiation, spectral lines) must be brought together to develop an understanding of basic atmospheric physics. Content. Structure of the atmosphere, the global energy balance, atmospheric thermodynamics, physics of weather patterns, observational techniques and instrumentation. Usually alternates with Astrophysics.

Role within programme and connections to other courses. This course introduces our students to a field where there are many opportunities for stimulating and satisfying careers. Medical physics is an application of physics to the particular — and particularly complex — system which is the human body. This course requires an integration of concepts from optics, quantum physics, nuclear physics, electromagnetism, mathematics, etc. Content. Radiation therapy, medical imaging. Usually alternates with Biophysics.

Role within programme and connections to other courses. This third, elective mechanics course can afford to take a more philosophical approach to Hamiltonian mechanics, while Mechanics II will, of necessity, be more pragmatic. In addition, our tools can now be used in a variety of very sophisticated circumstances.
Content. Topics might include Hamiltonian mechanics with greater reach, canonical transformations, Hamilton-Jacobi theory, action-angle variables, collision theory, non-linear mechanics and chaos, continuum mechanics (Lagrangian and Hamiltonian formulations, in contrast to the Continuum and Fluid Mechanics course).

Role within programme and connections to other courses. The Special Theory of Relativity is one of the foundations of modern physics. It underlies our understanding of particle physics and gravitation. This course builds beyond the introduction begun in the Physics course Mechanics I. It is recommended for all physics and mathematics students who wish to pursue the study of particles, fields and gravitation. Content. The course provides an introduction to the physical principles (Lorentz invariance, constancy of the speed of light, equivalence, of mass and energy) and the mathematical underpinnings (Minkowski spacetime, tensors), of the theory of special relativity. This course is cross listed MATH 3463. Credit cannot be obtained for both MATH 3463 and PHYS 3912.

Role within programme and connections to other courses. Solid state physics, also referred to as condensed matter physics, is the study of matter in which a large number of atoms (10²³ cm^-3) are bound together, forming a dense solid aggregate. It is a fundamental field of physics that leads to such areas and topics as material science, nanotechnology, and superconductivity. In this course, the student will study the structure of solids and how this structure affects such things as their mechanical properties, their thermal properties, and their electronic properties. This course builds on concepts introduced in thermodynamics and statistical physics, as well as quantum mechanics, with links to electromagnetism (e.g. van der Waals forces). Content. Lattice structure and dynamics, electron kinetics and dynamics, applications (e.g. semiconductors, superconductors, magnetic resonance). Usually offered on rotation with Atomic & Molecular Physics and Subatomic Physics.

Role within programme and connections to other courses. The study of biophysics offers a new perspective on physics through application to the biological sciences. It involves the integration of diverse concepts seen in introductory physics as well as elements of thermodynamics and fluid physics. It highlights the usefulness of physical thinking and a physicist’s perspective in the study of biological phenomena. Content. Biomechanics, the optics of vision, sound, hearing & echolocation, fluids in motion, the thermodynamics of life, physics at the cellular level, electricity and magnetism in biological systems. Usually alternates with Medical Physics.

Role within programme and connections to other courses. This second course on the formalism of electricity and magnetism extends the material from Electromagnetism I, and adds mathematical rigor and sophistication to our toolbox of techniques for electromagnetic problems. Heavier use of the ideas from Methods of Theoretical Physics is made, including Fourier methods and spherical harmonics. At the culmination of this course, we will have been exposed to all of the core ideas in E/M theory except for relativity. The latter and applications will follow in Electromagnetism III. Content. Fields in materials (D and H), polarization and magnetization vectors, polarizability and susceptibility tensors, types of magnetization, gauge theory, and its uses in solution of electromagnetic problems, conservation laws in electromagnetic theory, Poynting's theorem, the Maxwell stress-energy tensor, the Lagrangian for a charged particle in an electromagnetic field, radiation from accelerated charges, retardation effects, generation and propagation of E/M waves, the breakdown of classical electromagnetic theory.

Role within programme and connections to other courses. This is a capstone course to demonstrate the use of numerical and simulation techniques in a range of situations taken from across the programme. For instance, numerical solutions to differential equations might be used to look at some examples of chaotic behaviour or Monte-Carlo simulations might be used to look at percolative mass transport problems. Computational techniques have great importance in the modern physical sciences to the extent that some have described it as of equal importance to experimental and theoretical physics (although computational physics may also be considered to have elements of both theoretical and experimental physics, of course). The skills acquired in this course can subsequently be applied in other advanced courses, in particular the Advanced Research Project. Content. Numerical techniques, modelling techniques.

All physics honours students are required to complete a research project, under the supervision of a member of the department. Honours students in an interdepartmental program with physics may choose to complete their honours project in physics. Non-honours students may complete a research project as an elective. The Advanced Research Project course includes a formal written report and an oral defense, both of which are assessed by committee.

Role within programme and connections to other courses. The second QM course is not required for the majors programme, but furnishes our honours students with a range of tools allowing them to move beyond hydrogen-like atoms and to explore the applications of quantum mechanics.
Contents. Time independent perturbation theory, non-degenerate and degenerate cases, the Stark effect, fine structure, the Zeeman effect; the variational method, helium atom; the WKB method; time-dependent perturbation theory, Fermi's golden rule, harmonic perturbation, the adiabatic approximation, the Berry phase; a charged particle in EM field, gauge transformation, Landau levels, the Aharonov-Bohm effect; scattering theory: the Lippmann-Schwinger equation, optical theorem, partial wave expansion, phase shifts, effective range expansion, resonances, scattering between identical particles, Coulomb scattering.

A written report on the scientific activities of the work term. A component of the grade will be the employer's evaluation of the student. (Students must have a GPA of 2.7 or better for PHYS COOP placement.)

Role within programme and connections to other courses. Many physics career paths involve signal and image processing of some kind, e.g. seismic data processing, medical imaging, remote sensing (defense, forestry, mining), observational astrophysics, etc. As a result, understanding the possibilities and limitations of various data analysis techniques is a valuable asset for any physics graduate. Content. This course uses data from a variety of applications to illustrate the wide range of applicability of the tools discussed. Usually alternates with Advanced Electronics.

Role within programme and connections to other courses. The world of experimental physics is an electrifying blend of theory and hands-on measurements which relies heavily on a wide array of complex electronic devices. This course builds on Circuits & Elementary Electronics and introduces electronics and instrumentation we encounter through a physics career. The requirement to design and build electronic equipment, to integrate and control multiple components, and to efficiently operate complex instrumentation is fundamental to experimental physics. The goal of this course is to furnish the tools we need to meet these challenges. It includes topics in electronic design, interfacing and control, sensors and detectors, and data acquisition. Content. Multi-component design, amplifiers, filters, PCB design, integrated circuits, digital logic and programmable devices, radio frequency design, interfacing and control, transducers, detectors and receivers, solid state sensors. Usually alternates with Signal & Image Processing. 

A one-term research project, supervised by a member of the department, assessed on the basis of the research work carried out and a report. Note that no defense is involved (in contrast to the Advanced Research Project).

Role within programme and connections to other courses. Plasmas are sometimes referred to as the fourth state of matter. In a plasma, charge separation between electrons and ions gives rise to electric fields, and the movements of these charged particles result in currents and magnetic fields. Understanding the behaviour of plasmas involves mechanics, electromagnetism, and thermodynamics, and thus a plasma physics course contributes toward the overall goal of the physics programme by calling on us to combine knowledge from a variety of subfields of physics. Plasmas are found in many branches of physics (e.g. particle physics, condensed matter, astrophysics) and so the knowledge gained in this course will be of great value in many fields.
Content. Single particle motion, trajectories and drift, plasmas as fluids (electron fluid and ion fluid, single fluid magnetohydrodynamics), waves in a fluid plasma. Usually alternates with Continuum & Fluid Mechanics.

Role within programme and connections to other courses. This course pursues high level extension and application of electromagnetic theory. It connects to and extends relativistic mechanics (started in Mechanics I), and illuminates ideas from atomic/molecular physics, plasma physics and other fields. Content. Magnetohydrodynamics, relativistic four-vectors and four-tensors, force and Minkowski force, covariant formulation of E/M fields, an E/M perspective on quantum field theory.

This “course” is included in order to allow for ad hoc courses that might be offered only once. For instance, a visiting professor may have some expertise that s/he could share with the Department, or the student body may request a course about a particular topic that intrigues them. 

Role within programme and connections to other courses. Various courses will contain experiments that are directly related to the material addressed in the lectures, however, in the interest of promoting an understanding of connectivities (avoiding compartmentalisation) and refining research skills, this synthesis course will contain a variety of experiments, many of which integrate concepts learned in diverse courses. Content. The experiments will cover a wide variety of topics. 

Content. Relativistic quantum mechanics. The negative energy problem. Classical field theory, symmetries and Noether's theorem. Free field theory and Fock space quantization. The interacting field: LSZ reduction formula, Wick's theorem, Green's functions, and Feynman diagrams. Introduction to Quantum electrodynamics and renormalization. Credit cannot be obtained for both MATH 4443 and PHYS 4953. 

Role within programme and connections to other courses. The emphasis of this course will be on how what we know of Newtonian mechanics is carried over into a continuum. This approach helps to emphasise that the tools and knowledge we have already developed can be used to great effect in new situations. In addition to the portability of physical concepts, we will also be able to see some generally useful mathematical tools in a new context (vector calculus in velocity fields being a key example). Content. Volume and surface forces, stress and strain, Hooke’s Law, equation of motion for an elastic solid, longitudinal and transverse waves in a solid, fluid properties, fluid motion. Usually alternates with Plasma Physics.

Role within the programme and connections to other courses. Along with quantum theory, general relativity is one of the central pillars of modern theoretical physics with wide-ranging implications for astrophysics and high energy physics. The essential idea is that gravitation is a manifestation of the curvature of spacetime rather than a force in Newtonian sense. This course will provide students with a basic working understanding of general relativity and an introduction to important applications such as black holes and cosmology.
Content. Review and geometric interpretation of special relativity; foundations of general relativity; linearized gravity and classical tests; black holes; cosmology. Credit cannot be obtained for both MATH 4483 and PHYS 4983.

Role within programme and connections to other courses. This advanced quantum mechanics course introduces relativistic quantum mechanics and a variety of modern applications of quantum mechanics. Content. Relativistic quantum mechanics: the Klein-Gordon equation, Lorentz transformation, the Dirac equation, the Dirac solution of the hydrogen atom; quantum theory of radiation: radiation-matter interaction, decays, absorption, stimulated emission, scattering of photons by atoms, the Casimir effect; path integral formulation; quantum entanglement, the EPR paradox, dense coding, quantum teleportation, the Bell inequality.

Role within programme and connections to other courses. This advanced course draws upon electromagnetism, quantum mechanics and statistical thermodynamics to provide a capstone topic tied to the department’s research interests. Content. Principles of Magnetic Resonance Imaging, survey of imaging techniques, modern applications of MRI in medicine, biology and materials science.