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PHY Physics CoursesPHY100H
PHY100H1
In 1905 Einstein presented the first of 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 physics theory which is magical, and Einstein was not physics' only magician. We uncover the magic of the classical and the quantum world courtesy of Kepler, Newton, Maxwell, Einstein, Heisenberg and others. Topics include planetary motion, chaos, the nature of light, Schrodinger's cat, time travel, black holes, and quarks. No mathematics is required, and any necessary elementary classical physics is reviewed. PHY110Y
PHY110Y1
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 Physics. Students in other disciplines who wish some exposure to the methods and excitement of modern physics should consider either PHY100H or JPU200Y. (See "NOTE" after PHY100H giving description of laboratory) PHY138Y1
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; DC circuits; nuclear medicine; dose from radiation; nuclear physics. (See "NOTE" after PHY100H giving description of laboratory) PHY140Y1
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); planetary motion, gravitational collapse; black holes: Special Relativity and an introduction to elementary particle physics; the description of large numbers, e.g., a gas of weakly interacting particles (Statistical Mechanics); the breakdown of Newtonian mechanics in the microscopic world; introduction to Quantum Mechanics, wave-particle duality and the uncertainty principle. (See "NOTE" after PHY100H giving description of laboratory) PHY225H1
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. PHY238Y1
Electromagnetism; biological effects of radiation; physical optics; macroscopic phenomena; heat engines and metabolism. Examples are taken, where applicable, from the life sciences. PHY251H1
Point charges; Coulomb's inverse square law; electrostatic field and potential; Gauss' law; conductors; magnetostatistics; Ampere's law; Biot-Savart law; dielectric and magnetic materials; electrostatic and magnetostatic energy; Lorentz force; time varying fields; Faraday's law; Maxwell's equations. PHY252H1
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. PHY255H1
Complex notation; free, damped and forced vibrations; 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. PHY256H1
Failures of classical physics; Planck radiation formula; photoelectric effect; particle nature of waves; Compton scattering; wave nature of particles; atomic spectra; atomic energy levels; Schrodinger equation; solutions for one-dimensional systems (infinite well, square well, harmonic oscillator); time dependence; uncertainty principle; packets; scattering and tunnelling in one-dimension. PHY299Y1
Credit course for supervised participation in faculty research project. See page 42 for details. PHY305H1
The laboratory functions as an integrated lecture course/laboratory program. PHY307H1
Problem solving using Mathematica; introductory exercises; the physical pendulum, integration methods; the heat equation, finite difference methods; coupled spin systems, Monte Carlo methods; visualization and the statistical analysis of experimental data. PHY308H1
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. PHY309H1
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, Runge-Lenz algebra, harmonic and Morse oscillators. General techniques for computer-aided problem solving are developed. PHY315H1
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. PHY325Y1/326H1
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. PHY346H1
Linear systems analysis; transport in biological systems; control of the oculomotor system; electrical properties of nerves and membrane. Non-linear dynamics and simple neural networks. PHY351H1
Review of elementary mechanics, generalized co-ordinates and constraints, Lagrange's equations, Hamilton's principle, planetary motion, small oscillations and stability, Hamilton's equations, phase space, Liouville's theorem, canonical transformations, Hamilton-Jacobi theory, action-angle variables, invariant tori, perturbation theory. PHY352H1
Review of vector calculus, transformation properties of vectors, electrostatics, special theory of relativity, development of the equations of electrodynamics from the Einstein principle of relativity and the laws of electrostatics, basic formulae of magnetostatics, electromagnetic plane waves, and, in the unlikely event that time permits, retarded potentials and radiation. PHY353H1
Review of Maxwell's equations; waves in free space; 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; energy and momentum of E-M waves; geometrical optics; interference, coherence effects; interferometers; Fraunhofer and Fresnel diffraction; Fourier optics; holography. PHY355H1
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. PHY357H1
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. PHY358H1
Variational principle; fine and hyperfine structure of the hydrogen atom; the helium atom; exchange terms; coupling schemes; Hund's rules; simple molecules; ortho and para states; bonding and antibonding orbitals; rotation and vibration of molecules; crystal binding; electron in a periodic potential; reciprocal lattice; Bloch's theorem; Kronig-Penney model and energy bands; metals, semiconductors and insulators; Fermi surfaces; chemical potential. This course is not a prerequisite for any PHY 400-level course. PHY359H1
Designed for students interested in the physics of the Earth and the planets. Study of the Earth as a unified dynamic system; determination of internal divisions in the planet; age and thermal history of the planet; Earth's magnetic field and its origin; earthquakes and seismology; Earth's gravitational field and the concept of isostasy; development and evolution of the Earth's large scale surface features (plate tectonics, plate loading and flexure). PHY371Y1/372H1
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. PHY406H1
The laboratory functions as an integrated lecture course/laboratory program. PHY407H1
Problem solving using Mathematica; introductory exercises; the physical pendulum, integration methods; the heat equation, finite difference methods; coupled spin systems, Monte Carlo methods; visualization and the statistical analysis of experimental data. PHY408H1
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. PHY409H1
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. PHY425Y1/426H1
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 PHY325Y and is open from 9:00am. - 5:00pm, Monday to Friday. PHY445H1
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. Three student labs are held in the imaging research laboratories at Sunnybrook Hospital. Students not in a physics specialist program should consult the coordinator about the recommended background. PHY457H1
Quantum dynamics in Heisenberg and Interaction Pictures; Coherent States, Electron in a Magnetic Field; Continuous and Discrete Symmetries in Quantum Mechanics; Bloch's Theorem, Localized States in a Disordered Lattice; Green's Function Method; WKB Approximation, Rayleigh-Schrodinger and Brillouin-Wigner Perturbation Theory; Time Dependent Perturbation Theory, Fermi's Golden Rule; Absorption and Emission of Light from Atoms; Variational Techniques; Scattering Theory, Lippman-Schwinger Equation, Partial Wave Analysis, S-Matrix and T-Matrix Theory. PHY459H1
Thermal equilibrium and temperature; equations of state; entropy; free energies; Maxwell relations; phase transitions; third law; superfluids; superconductors; elements of hydrodynamics; conservation laws; solenoidal and irrotational flow; entropy production; constitutive relations; Navier-Stokes equation. PHY460H1
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. PHY471Y1/472H1
These self-study courses are similar to PHY371Y/372H, at a higher level. PHY478H1/479Y1
An introduction to research in Physics. For further information contact the Associate Chair, Undergraduate Studies. PHY480H1
Topics include: 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. PHY481H1
Topics include: thermodynamic fluctuations, distribution functions, interacting classical fluids, phase transitions, Ising model, mean field theory, scaling and universality. PHY482H1
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. PHY483H1
Topics include: special theory of relativity, Lorentz transformations, kinematics, energy-momentum tensor and hydrodynamics; relativistic particle dynamics, and electrodynamics, introduction to gravitation theory, geodesics, curvature tensor and Bianchi identities; variational principle and Einstein's gravitational field equations; gravitational waves. PHY484H1
Topics include: General theory of relativity; Schwarzschild solution, Kruskal coordinates, gravitational collapse and black holes. Experimental tests of gravitational theories. Cosmology; Friedmann-Robertson-Walker metric, Hubble red-shifts. Current models in Cosmology. PHY485H1
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. PHY486H1
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 solution 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. PHY487H1
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. PHY488H1
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. PHY489H1
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. PHY490H1
Introductory aspects of Nuclear Physics and quantum chromodynamics, nuclear force, bulk properties of nuclei, nuclear transitions, nuclear structure, nuclear reactions. PHY491H1
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. PHY493H1
This course covers wavefield and ray approximation methods for imaging the interior of the Earth using seismology. PHY494H1
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. PHY495H1
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). PHY496H1
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. PHY497H1
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. PHY498H1
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. PHY499H1
Topics include: review of radiation; satellite orbits; scanning geometries; remote sensing and the atmosphere effect; visible, microwave, and infra-red techniques; remote sounding; scanning techniques; the retrieval problem; microwave, ultra-violet, and infra-red techniques; advanced techniques. |
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