## PHY Physics Courses
Undergraduate seminar that focuses on specific ideas, questions, phenomena or controversies, taught by a regular Faculty member deeply engaged in the discipline. Open only to newly admitted first year students. It may serve as a distribution requirement course; see page 40.
In 1915 Einstein presented a quartet of papers which revolutionized our understanding of gravity. He commented: “Hardly anyone who has truly understood this theory will be able to resist being captivated by its magic.” The General Theory of Relativity is not the only theory of physics which is magical, and Einstein was not physics’ only magician. We uncover the wonders of the classical and the quantum world courtesy of Galileo, Newton, Maxwell, Einstein, Heisenberg and others. Topics include planetary motion, chaos, the nature of light, time travel, black holes, matter waves, Schrodinger’s cat, and quarks. No mathematics is required, and any necessary elementary classical physics is reviewed.
Designed for students who do not intend to take more than one course in Physics, but who wish to acquire a working knowledge of basic physics needed in other areas of science. The course is offered at a level similar to OAC or new Grade 12 Physics. Students in other disciplines who wish some exposure to the methods and excitement of modern physics should consider either PHY100H1 or JPU200Y1. (See “NOTE” after PHY100H1 giving description of laboratory.)
This course is recommended strongly for students following a life science program.
This course introduces topics in physics relevant for life sciences. Mechanics;
torque and statics; work, power and energy; viscous forces; vibrations
and waves; sound; optics; electric and magnetic forces and fields; dielectric
and conductors; nuclear medicine; dose from radiation; nuclear physics.
(See “NOTE” after PHY100H1 giving description
of laboratory.)
The first physics course in many of the Specialist and Major Programs in Physical Sciences. It provides an introduction to the concepts, approaches and tools the physicist uses to describe the physical world while laying the foundation for classical and modern mechanics. Topics include: the motion of single particles and rigid, extended bodies (Newtonian Mechanics); the concepts of force, work, and energy; simple harmonic motion; planetary motion, gravitation; black holes; special relativity; an introduction to elementary particle physics; electrostatics; the breakdown of Newtonian mechanics in the microscopic world; atomic and nuclear physics; an introduction to Quantum Mechanics, wave-particle duality and the uncertainty principle. Students take the Physics Specialist Laboratory in alternating weeks. The first component consists of dynamics and mechanics experiments in our new micro-computer based laboratory. The second component consists of a free choice experiments chosen from a list of basic experimental techniques, standard and classic experiments.
A general, non-mathematical introduction to many of the most interesting concepts of physics with an emphasis on modern physics, intended primarily for non-science students. It focuses on basic changes in our view of the universe that are needed to accommodate important discoveries of 20th-century Physics, and introduces some of the striking parallels to ideas of Eastern mysticism. Topics include Newtonian physics, space-time, relativity, black holes, quantum physics, chaos, origin and fate of the universe. The relationship of physics to linguistics, the humanities and the social sciences is also discussed. (Given by the Department of Physics and University College) This course entails the writing of essays and written tests.
The 2nd year Physics Laboratory. Topics including experimental techniques, instrumentation, and data analysis are introduced through experiments, complementary lectures, and library research of some of the great experiments of physics.
See “Division of the Environment”
Electromagnetism; biological effects of radiation; physical optics; macroscopic phenomena; heat engines and metabolism. Examples are taken, where applicable, from the life sciences.
Point charges; Coulomb’s Law; electrostatic field and potential; Gauss’ Law; conductors; electrostatic energy; magnetostatistics; Ampere’s Law; magnetostatic energy; Lorentz Force; Faraday’s Law; dielectric and magnetic materials; Maxwell’s equations.
The quantum statistical basis of macroscopic systems; definition of entropy in terms of the number of accessible states of a many particle system leading to simple expressions for absolute temperature, the canonical distribution, and the laws of thermodynamics. Specific effects of quantum statistics at high densities and low temperatures.
Complex notation; free, damped and forced harmonic oscillations; resonance; AC circuits; coupled oscillators; normal modes; travelling waves; simple harmonic wave; wave equation; wave impedance; transverse and longitudinal waves; flow of energy in waves; reflection and transmission at interfaces; group and phase velocity; Fourier series and Fourier transforms.
Failures of classical physics; the Quantum revolution; Stern-Gerlach effect; harmonic oscillator; uncertainty principle; interference packets; scattering and tunnelling in one-dimension.
Credit course for supervised participation in faculty research project. See page 40 for details.
Principles of Human Physiology with tutorials on the biophysical concepts applied to physiological processes. Restricted to students enroled in the Biophysics and Physiology (Theoretical) programs.
Introduction to methods for remote sensing of buried archaeological remains, (magnetics, resistivity, electromagnetics), dating (Carbon 14, TL, ESR, etc.) and analysis (X-Ray, INAA) of ancient materials. Application of methods and interpretation of results in archaeological contexts. Issues of art and authenticity are also addressed. Course includes a laboratory component. (Not offered every year) (Given by the Departments of Physics and Anthropology)
Introduction to the principles behind archaeometric methods for remote sensing, dating, and analysis of archaeological materials, and interpretation of results. Course includes both field and in-house laboratory components. Offered in conjunction with JPA305H1. (Not offered every year) (Given by the Departments of Physics and Anthropology)
The laboratory functions as an integrated lecture course/laboratory program. Passive linear circuits: theorems, networks, and equivalents; meters, transient and steady responses, power, transformers, transmission lines. Digital devices: gates logic, Boolean algebra, minimization, flip-flops, counters, delays. Op-amps: dependent sources, amplifiers, integrators, feedback, slew rate, filters. Diodes: peak detector, rectification, regulators. Noise: sources, grounding, shielding, ground loops. Transistors: characteristics, analysis, amplifier design.
Problem solving with computers, using both algebraic and numerical methods. After a brief introduction to the basic techniques, various physics problems are treated with increasingly more sophisticated techniques. Examples include the physical pendulum, heat equation, quantum mechanics, Monte Carlo simulation, differential equation, and graphical presentation of results.
The analysis of digital sequences; filters; the Fourier Transform; windows; truncation effects; aliasing; auto and cross-correlation; stochastic processes, power spectra; least squares filtering; application to real data series and experimental design.
Classic quantum mechanics problems are explored using Maple computer algebra and graphics. These include bound state and scattering problems in 1D, angular momentum and spin, commutator algebra, scattering in 3D and time dependent processes. General techniques for computer-aided problem solving are developed.
The role of radiation in the generation, maintenance and evolution of planetary atmospheres and climate: Radiation laws, absorption and emission. Simple radiative exchange processes and atmospheric models. Energy balance. Radiation and climatic change. Comparative radiation studies in planetary atmospheres. Pollution and man-made effects.
Experiments in this course are designed to form a bridge to current experimental research. A wide range of experiments are available using contemporary techniques and equipment. In addition to the standard set of experiments a limited number of research projects are also available. The laboratory is open from 9 a.m. - 5 p.m., Monday to Friday.
Complex nature of the scientific method; inter-connection between theory, concepts and experimental data; characteristics of premature, pathological and pseudo-science; public perception and misperception of the scientific method; the supposed end of the Golden Era of Science; the insufficiency of reductionism; trends in modern science. (Offered in alternate years with PHY342H1)
Topics of current prominence in the physical sciences and mathematics are discussed. Topics change each year as the sciences evolve. Appropriate topics might include: high-temperature superconductivity, cosmology, chaos and non-linear dymanics. (Offered in alternate years with PHY341H1)
Linear systems analysis; transport in biological systems; control of the oculomotor system; electrical properties of nerves and membrane. Introduction to chaos in biological systems.
Symmetry and conservation laws, stability and instability, generalized co-ordinates, Hamilton’s principle, Hamilton’s equations, phase space, Liouville’s theorem, canonical transformations, Poisson brackets, Noether’s theorem.
Review of vector & tensor calculus, transformation properties of vectors & tensors, electrostatics, basic formulae of magnetostatics, electrodynamics (Maxwell’s Equations), gauge transformations of scalar & vector potentials, retarded potentials, Lie’nard-Wiechert potentials, radiation, special theory of relativity, relativistic mechanics and relativistic electrodynamics.
Review of Maxwell’s equations; electric fields in matter; magnetic fields in matter; electromotive force; electromagnetic induction; electromagnetic waves in vacuum; waves in dielectric and conductive materials, skin effect; waves in dispersive media: polarization phenomena; Fresnel equations; reflection and refraction from an interface; Brewster angle, total internal reflection; interference, coherence effects; interferometers; Fraunhofer and Fresnel diffraction; waveguides, optical fibres, radiation.
The general structure of wave mechanics; eigenfunctions and eigenvalues; operators; orbital angular momentum; spherical harmonics; central potential; separation of variables; hydrogen atom; Dirac notation; operator methods; harmonic oscillator and spin.
The subatomic particles; nuclei, baryons and mesons, quarks, leptons and bosons; the structure of nuclei and hadronic matter; symmetries and conservation laws; fundamental forces and interactions, electromagnetic, weak, and strong; a selection of other topics, CP violation, nuclear models, standard model, proton decay, supergravity, nuclear and particle astrophysics. This course is not a prerequisite for any PHY 400-level course.
Quantum theory of atoms, molecules, and solids; variational principle and perturbation theory; hydrogen and helium atoms; exchange and correlation energies; multielectron atoms; simple molecules; bonding and antibonding orbitals; rotation and vibration of molecules; crystal binding; electron in a periodic potential; reciprocal lattice; Bloch’s theorem; nearly-free electron model; Kronig-Penney model; energy bands; metals, seminconductors, and insulators; Fermi surfaces. This course is not a prerequisite for any PHY 400-level course.
Designed for students interested in the physics of the Earth and the planets. Study of the Earth as a unified dynamic system; determination of major internal divisions in the planet; development and evolution of the Earth’s large scale surface features through plate tectonics; the age and thermal history of the planet; Earth’s gravitational field and the concept of isostasy; mantle rheology and convection; Earth tides; geodetic measurement techniques, in particular modern space-based techniques.
An individual study program chosen by the student with the advice of, and under the direction of, a staff member. A student may take advantage of this course either to specialize further in a field of interest or to explore interdisciplinary fields not available in the regular syllabus.
An instructor-supervised group project in an off-campus setting. See page 40 for details.
An introduction to research in archaeometry and archaeological prospecting. Possible projects: magnetic and resistivity surveying of archaeological sites; thermoluminescence measurements; neutron activation analysis and x-ray fluorescence analysis of artifacts; radiocarbon dating by atom counting; lead isotope analysis. (Not offered every year) (Given by the Departments of Physics and Anthropology)
The course functions as an integrated lecture/laboratory program. How best to use computers in the lab to improve experiments. Lectures include basic and practical case studies: computer as controller and data collector; programming and interface methodologies; the principles of analog-to-digital and digital-to-analog conversion; data analysis; signal processing techniques. Labview is used extensively.
Problem solving with computers, using both algebraic and numerical methods. After a brief introduction to the basic techniques, various physics problems are treated with increasingly more sophisticated techniques. Examples include the physical pendulum, heat equation, quantum mechanics, Monte Carlo simulation, differential equation, and graphical presentation of results.
The analysis of digital sequences; filters; the Fourier Transform; windows; truncation effects; aliasing; auto and cross-correlation; stochastic processes; power spectra; least squares filtering; application to real data series and experimental design.
Classic quantum mechanics problems are explored using Maple computer algebra and graphics. These include bound state and scattering problems in 1D, angular momentum and spin, variational methods, scattering in 3D and time dependent processes. General techniques for computer-aided problem solving are developed.
Experiments in this course are designed to form a bridge to current experimental research. A wide range of experiments are available using contemporary techniques and equipment. In addition to the standard set of experiments and limited number of research projects are also available. The laboratory is a continuation of PHY325/326 and is open from 9:00am. - 5:00pm, Monday to Friday.
An introduction to the geophysical exploration of the subsurface. Topics covered include gravity, seismic, magnetic, electrical and electromagnetic surveying and their application in prospecting, hydrogeology, and environmental assessments. This course is intended primarily for geological engineering and geology students.
The mathematical, physical and engineering basis for medical imaging is introduced by combining the mathematical description of linear systems with the physics of imaging systems utilizing x-rays, ultrasound, and magnetic resonance techniques. The combination of mathematics and physics that has lead to the development of modern medical imaging systems is emphasized. Data for problem sets and labs will be processed using MATLAB software. Students not in a physics specialist program should consult the lecturer about the recommended background
Quantum dynamics in Heisenberg and Schrodinger Pictures; WKB approximation; Variational Method; Time-Independent Perturbation Theory; Spin; Addition of Angular Momentum; Time-Dependent Perturbation Theory; Scattering.
The three laws of thermodynamics; the inexorable increase of entropy, phases and phase transitions. Fluid mechanics, the Navier-Stokes equations; dynamical similarity, rotating flows, vorticity, waves, instabilities and turbulence.
Nonlinear oscillator; nonlinear differential equations and fixed point analysis; stability and bifurcation; Fourier spectrum; Poincare sections; attractors and aperiodic attractors; KAM theorem; logistic maps and chaos; characterization of chaotic attractors; Benard-Rayleigh convection; Lorenz system.
These self-study courses are similar to PHY371Y1/372H1, at a higher level.
An introduction to research in Physics. For further information contact the Associate Chair, Undergraduate Studies.
Classical and quantum statistical mechanics of noninteracting systems; the statistical basis of thermodynamics; ensembles, partition function; thermodynamic equilibrium; stability and fluctuations; formulation of quantum statistics; theory of simple gases; ideal Bose and Fermi systems.
Topics include: the origin and implications of symmetry in physics; the basic language of group theory; discrete groups and matrix groups; groups of physical transformations; the representation of groups; tensor operators and the Wigner-Eckart theorem; Lie groups. Applications to some of the following: crystal symmetries; electronic bands in crystals; vibrations of molecules; SU(2) and SU(3) in particle and nuclear physics.
Basis to Einstein’s theory: differential geometry, tensor analysis, gravitational physics leading to General Relativity. Theory starting from solutions of Fchwarzchild, Kerr, etc.
Applications of General Relativity to Astrophysics and Cosmology. Introduction to black holes, large scale structure of the universe.
Lasers, and the interaction of light with matter. In addition to the semiclassical theory of the laser, linear and nonlinear optical elements ranging from optical resonators to acousto-optic modulators, along with a survey of laser types and their applications are discussed. A number of modern topics from quantum optics, including laser cooling, squeezed light and the Einstein-Podolsky-Rosen effect are also considered.
Introduction to quantum electrodynamics, quantization of the electromagnetic field; semiclassical picture of atom-radiation field interaction, Einstein coefficients, laser theory from the Einstein rate equations; resonance interaction of light with two-level atoms, optical soliton propagation, coherent and squeezed states of light, quantum theory of atom-radiation field interactions, radiative decay and the Lamb shift, photonic band gap materials and quantum theory of the laser.
Introduction to the concepts used in the modern treatment of solids. The student is assumed to be familiar with elementary quantum mechanics. Topics include: crystal structure, the reciprocal lattice, crystal binding, the free electron model, electrons in periodic potential, lattice vibrations, electrons and holes, semiconductors, metals.
Introduction to quantum field theory and elementary particle physics. Topics include: canonical quantization, symmetries and conservation laws, S-matrix expansion, Feynman diagrams, Dirac equation, gauge invariance, quantum electrodynamics and, if time permits, an introduction to nonabelian gauge theories and weak interactions.
This course surveys the experimental basis and theoretical framework of the “Standard Model” of Particle Physics and its possible extensions. Topics include the standard electroweak model, scattering and parton distributions, strong interactions and quantum chromodynamics.
Review of conventional, textbook quantum mechanics. Formal measurement theory and wave function collapse; quantum states and nonseparability, violation of local casuality, Bell theorems, “quantum tricks”, decoherence and the emergence of classical behaviour. Hidden variables, deBroglie-Bohm theory and generalizations; many-worlds interpretation and other theories of “beables”. Consistent histories approach of Omnes and Gell-Mann and Hartle; nature of “True” and “Reliable” statements.
This course covers wavefield and ray approximation methods for imaging the interior of the Earth (including hydrocarbon reservoirs and mineral deposits) using seismology.
How to investigate Earth structure at depths ranging from meters to tens of kilometers using gravity, magnetic, electrical, electromagnetic and nuclear geophysical methods. Current methodologies and the theoretical basis for them are presented.
This course deals with the numerical analysis of data associated with space geodesy, earthquake seismology, geomagnetism and palaeomagnetism, isotope geochronology, as well as numerical simulations of a wide variety of geodynamic processes (e.g. mantle convection, post-glacial rebound, Earth tides).
A laboratory course (with introductory lectures) dealing with physical methods for exploring Earth structure; i.e., seismic, gravity, magnetic, electrical, electromagnetic, and nuclear methods. It is designed to give “hands on” experience with the techniques of geophysical data analysis as well as data acquisition.
Topics include: the equations of classical hydrodynamics: conservation of mass, momentum, and energy; Bernoulli’s theorem; Ertel’s theorem; nondimensional analysis, dynamics of stratifield flow: static stability; convection; shear flow instability and the Miles-Howard theorem; internal gravity waves; gravity wave drag and Eliassen-Palm theorem; introduction to dynamics of rotating, stratified flow and baroclinic instability.
Topics include: thermodynamics of water substances in the atmosphere; nucleation of liquid water in water vapour and condensation nuclei; nucleation of the ice phase and ice nuclei; growth of cloud droplets and ice particles; initiation of precipitation particles; precipitation processes; role of clouds in atmospheric circulations; effects of latent heat release in PV distribution; concept of CISK; examples of CISK driven systems.
Introduction to satellite observations; satellite orbits; scanning geometries; blackbody radiation; radiative transfer; ultraviolet, visible, infrared, and microwave techniques; active vs. passive remote sounding techniques; imaging, non-imaging, and sounding instruments; the inverse problem; nadir vs. limb sounding; remote sounding of atmospheric temperature, composition, aerosols, clouds, precipitation, and wings; remote sensing of the Earth’s surface; discussion of selected satellite missions. |

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