Program and Course Descriptions
(University of Toronto, Canada)

Content:

Introduction

Physics is the study of natural phenomena at the most fundamental level. Physicists investigate the properties of the states of matter and the structure and behaviour of the components of matter. The gravitational, electromagnetic and nuclear interactions are examined and different systems of mechanics including classical, relativistic, quantum and statistical, are developed to describe interactions between systems ranging from sub-atomic to galactic in size.

Physics is an experimental science. All physics students are introduced to the skills of the experimentalist in several varied laboratories. Physics students must also develop considerable fluency in mathematics and computational techniques. Theories are often developed in terms of mathematical models: these idealizations of reality are treated concisely and quantitatively using analytical and numerical methods.

A background in Physics is useful in a wide range of disciplines, from Archaeology through Philosophy to Zoology. A knowledge of Physics is a powerful tool for students considering a career in the Environmental or Life Sciences. An understanding of Physics is essential for those who are concerned about important social issues affected by the impact of modern technology.

The Physics Specialist Program has recently been revised. Students take a core program to the end of third year. In fourth year, students intending to undertake graduate studies are strongly encouraged to take an Option. Options are offered in Quantum Optics and Condensed Matter Physics, Sub-Atomic Physics and Planetary Physics, reflecting the research excellence of the faculty.

Quantum Optics is the study and application of optical photons as generated by lasers, which emit beams with high coherence and high intensity. Laser science is an essential component in spectroscopy, telecommunications, surgery, material processing, entertainment, holography, environmental diagnostics and inertial confinement fusion reactors. The importance of Quantum Optics in Ontario has been recognized by the formation of the Ontario Laser and Lightwave Research Centre, one of 7 Centres of Excellence created by the Ontario Government in 1988.

Condensed Matter Physics is the study of solids and liquids. The scope of modern liquid state physics and soft matter physics encompasses simple and complex fluids, liquid crystals, polymers, gels and microemulsions. Modern condensed matter physics also includes nonequilibrium phase transitions, nonlinear dynamic instabilities and chaos. The entire field has a strong link to materials science and engineering where many fundamentals of condensed matter physics have found a broad range of technologically advanced applications.

Sub-Atomic Physics is the study of the fundamental structure of matter. The field is divided in two complementary studies of nuclear matter and high-energy, elemantary particle physics. Together, they represent the Frontier of our understanding of the universe and of what it is comprised.

A large number of fundamental research questions are under active investigation in the field. The study of nuclear matter under extremes and of nuclear reactions that govern stellar evolution are some of the areas where our understanding is rapidly evolving. At a more fundamental level, the question of whether quarks and leptons are really the most fundamental constituents of our universe, or what the concept of mass actually means, continue to challenge our immagination as well as our technical ability.

A student interested in the Sub-Atomic Physics option should consider enroling in PHY488, PHY489 and PHY490. More theorethically motivated students can also consider taking one or more of PHY482 and PHY483. PHY488 is an elementary primer to Quantum Field Theory and Quantum Electrodynamics in which both photons and electrons are treated relavistically. PHY489 covers the physics of quarks, leptons, gluons, photons, intermediate vector bosons and gravitons. PHY490 is an introduction to nuclear structure and reactions as well as to quantum chromodynamics. The concept of symmetries, which play an important role in many areas of physics, is explored in PHY482 and an introduction to relativity theory is provided in PHY483 and PHY484.

While we encourage students to take both nuclear and high-energy physics courses as toghether they provide a good introduction to the whole of sub-atomic physics, individual programs can be tailored to individual interests.

The Earth is an exceptional planet, especially because of the life-sustaining interplay between solid earth, oceans and atmosphere. Physicists have been leaders in recent dramatic improvements in understanding how this complex system came into being, how it functions, and how it will change. Through a combination of theoretical insight, high tech instrumentation and sophisticated computer modelling, earth scientists seek to describe not only global processes, but also the environmental and economic implications in our day-to-day existence. Since most of the earth's interior is inaccessible to direct observation, many aspects of its structure and evolution remain enigmatic. As a consequence, scientists employ a multitude of physical principles to study the Earth indirectly. Seismologists consider the travel of sound waves through the Earth, such as those generated by earthquakes. Geodynamicists investigate the movement of the outer shell of the planet, and the link between this motion and internal driving forces. Applied geophysicists use a variety of physical imaging procedures to assist in petroleum and mineral exploration, and solve many different environmental problems. Atmospheric physicists observe pollution in the atomosphere from remote sensing devices orbiting the planet.

The Professional Experience Year program is available to eligible, full-time Specialist students after their second year of study.

The Department produces an Undergraduate Reference Booklet which gives detailed information on programs and courses, and describes the operation of the Department and the counselling services available.

Associate Chair: Professor H.M. van Driel, Room 324, McLennan Physical Laboratories [+1 (416) 978-6674]

Enquiries: Undergraduate Office, Room 301, McLennan Physical Laboratories [+1 (416) 978-7057/5219]

Physics Programs

Enrolment in the Physics programs requires completion of four courses; no minimum GPA is required.

Physics (B.Sc.)

Specialist program: S19441 (12.5 full courses or their equivalent, including at least one 400-series course)

First Year: MAT 137Y/157Y, 223H; PHY 140Y

Second Year: MAT 237Y, 244H; PHY 225H, 251H, 252H, 255H, 256H

Third Year: APM 346H; MAT 334H; PHY 351H, 352H, 353H, 355H, 357H/358H

Fourth Year: PHY 457H, 459H/460H

NOTE: Third/Fourth Year Laboratories:

All specialists must take a minimum of 1.5 courses in practical physics in third/fourth year. One half- course must be in the Quantum Physics Laboratory. The laboratory courses are offered in units of a half- course and up to 3 half-courses in any one laboratory may be taken.

Quantum Physics Laboratory: PHY 325Y/326H, 425Y/426H

Electronics Laboratory: PHY 305H, 405H/406H

Computational Laboratory: PHY 307H/308H, 407H/408H

Fourth Year Physics Options

NOTE: The Department of Physics offers to senior undergraduate students wishing to specialize in a particular area of Physics a limited set of options. An option, the equivalent of 2 full courses, is built up from Advanced Courses commonly offered to incoming graduate students, in the series PHY480H - 499H, a half or full-year Undergraduate research project PHY478H/479Y and the open format supervised reading courses PHY471Y/472H. An option is NOT required to complete a Specialist Program in Physics but is recommended strongly to students wishing to pursue further graduate studies. Entry to an option requires an interview with one of the option supervisors and permission of the Department. An above average performance in the equivalent of a Specialist or combined Specialist Program in Physics is expected. Option talks are given to students in their third year of study. An option can be tailored for each student.

Physics Course Descriptions

NOTE: Books listed in course descriptions will not necessarily be the texts for the course, but do indicate the level of presentation.

NOTE: First Year Laboratory
Taken by all students enrolled in PHY 110Y, 138Y, 140Y. An introductory course in experimentation, starting with a selected experiment, which each student is obliged to complete, but from there on, offering choices. Emphasis is on the general principles of experimentation: planning, use of instruments, error estimation, data analysis and comparison with theory, the keeping of complete records, and genuine exploratory work. Laboratories are given in alternate weeks; students taking Physics and Chemistry laboratories may schedule these on the same afternoon of alternate weeks.

PHY140Y
Physics! 78L, 39P, 26T

The first course in the Physics Specialist and Major Programs. Topics include: Newton's laws in vector form for particles; conservation of energy, linear and angular momentum; simple harmonic motion and waves; optics; planetary motion; gravitational collapse; black holes; the special theory of relativity; elementary particles; nuclear forces; electric and magnetic fields; kinetic theory of gases; Maxwell-Boltzmann distribution; chaos; breakdown of classical mechanics; wave-particle duality; uncertainty principle; quantization.
Exclusion:PHY100H/110Y/138Y
Prerequisite: OAC Calculus and OAC Physics
Co-requisite: MAT137Y/157Y, (MAT223H/240H recommended)

PHY225H
Fundamental Physics Laboratory 26L, 78P

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.
Prerequisite: PHY138Y/140Y
Co-requisite: Any second year PHY offering

PHY251H
Electricity and Magnetism 26L, 13T

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.
Exclusion: PHY238Y
Prerequisite: PHY138Y/140Y
Co-requisite:MAT235Y/237Y/257Y

PHY252H
Thermal Physics 26L, 13T

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.
Reference: Kittel and Kroemer, Thermal Physics
Prerequisite: PHY138Y/140Y
Co-requisite: MAT235Y/237Y/257Y

PHY255H
Oscillations and Waves 39L

Complex notation; free, damped and forced vibrations; reduction to linear systems; resonance; AC circuits; mutual inductance, 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.
Prerequisite: PHY138Y/140Y
Co-requisite: MAT235Y/237Y/257Y, (MAT244H recommended)

PHY256H
Introduction to Quantum Physics 39L

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.
Reference: French & Taylor, An Introduction to Quantum Physics
Prerequisite: PHY138Y/140Y
Co-requisite: MAT235Y/237Y/257Y, (MAT223H/240H recommended)

PHY325Y/326H
Modern Physics Laboratory 56L/78P

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.
Prerequisite: PHY225H, 251H, 256H

PHY351H
Classical Mechanics 26L, 13T

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.
Reference: Marion and Thornton, Classical Dynamics; Percival and Richards, Introduction to Dynamics, Cambridge
Prerequisite: MAT244H/249H, PHY255H

PHY352H
Electromagnetic Theory 26L, 13T

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.
Prerequisite: MAT223H/240H/244H, PHY251H, 255H

PHY353H
Electromagnetic Waves and Radiation 26L, 13T

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; thin film optics; Fraunhofer and Fresnel diffraction; Fourier optics; holography.
Prerequisite: PHY352H

PHY355H
Quantum Mechanics I 26L, 13T

The general structure of wave mechanics; Dirac notation; operator methods; central potential; relative and centre of mass motion; separation of variables; orbital angular momentum; spherical harmonics; the Hydrogen atom; the three-dimensional oscillator; spin; identical particles; symmetry; addition of spins; stationary-state perturbation theory.
Reference: Cohen-Tannoudji, Quantum Mechanics, Vol. 1, Wiley
Exclusion: CHM321Y
Prerequisite: MAT223H/240H/244H; PHY251H, 256H/CHM225Y/229H

PHY357H
Nuclear and Particle Physics 26L, 13T

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.
Prerequisite: PHY355H

PHY425Y/426H
Advanced Modern Physics Laboratory 156/78P

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.

Background: This course is a sequel to PHY325Y/326H in which the students can perform the more advanced experiments available in the laboratory and take more initiative in their design and execution. Students are expected to learn in depth a small area of physics by performing an experiment and reading the relevant material needed to understand the physics involved. The report-writing skills and ability to keep a clear research notebook learned in PHY325Y-326H are expected to be exercised at a more advanced level. Students are encouraged to consider the experiments as open-ended and attempt to carry out measurements other than those described in the manual.

Topics: Experiments available include: a number of studies of x-ray diffraction and x-ray fluorescence; the infrared spectra of diatomic molecules, fundamental and overtone spectrum of HCl; atomic and molecular spectra; Fourier transform spectroscopy; optical pumping; ionization studies with a mass spectrometer; Raman effect; nuclear magnetic resonance; nuclear quadrupole resonance; electron spin resonance; electron microscope; scanning tunneling microscope; Brillouin spectroscopy; the He-Ne laser; fiber optics; superconductivity; magnetoresistance; the Hall effect of seiconductors; low temperature thermal expansion; the Mossbauer effect; and other atomic, molecular and solid state experiments. Nuclear and particle physics experiments include the study of radioactivity, alpha-ray spectroscopy, neutron diffusion in water bath, production and study of artificial radioactive sources using the Slowpoke reactor, high resolution gamma spectroscopy with Ge detectors, and muon lifetime measurements.
Prerequisite: PHY325Y/326H

PHY457H
Quantum Mechanics II 39L

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.
Prerequisite: PHY355H

PHY460H
Nonlinear Physics 26L, 13T

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.
Prerequisite: PHY351H

The Advanced Courses

PHY482H
Symmetries in Physics 26L

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; rotations and SU(2); tensor product representations; projective representations; tensor operators and the Wigner-Eckart theorem; the character of a representation; Lie groups; algebraic methods in quantum mechanics; conservation laws. Applications will be made to some of the following: crystal symmetries; electronic bands in crystals; vibrations of molecules; SU(2) and SU(3) in particle and nuclear physics (bosons and fermions; the atomic and nuclear shell models; the quark model).

PHY483H
Relativity Theory I 26L

Topics include: special theory of relativity, Lorentz transformations, kinematics, energy-momentum tensor and hydrodynamics; relativistic particle dynamics, and electrodynamics. Introduction to gravitation theory, tensors and tensor densities, covariant differentiation, parallel displacement law, geodesics, curvature tensor and Bianchi identities; variational principle and Einstein's gravitational field equations; linear approximation to Einstein's equations and gravitational waves.

PHY488H
Introduction to Particle Theory 26L

Introduction to quantum field theory and elementary particle physics in which both photons and electrons are treated relativistically. 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. At the end of the course, students should be able to perform simple Feynman calculations of cross sections and scattering amplitudes, and are introduced to the electroweak Lagrangian and QCD.

PHY489H
Introduction to High Energy Physics 26L

This course surveys the experimental basis and theoretical framework of the "Standard Model" of Particle Physics and its possible extensions. Topics will include the standard electroweak model, scattering and parton distributions, strong interactions and quantum chromodynamics.

PHY490H
Introductory Nuclear Physics 26L

Introductory aspects of Nuclear Physics and quantum chromodynamics, nuclear force, bulk properties of nuclei, nuclear transitions, nuclear structure, nuclear reactions.

Mathematics Course Descriptions

MAT137Y
Calculus! 78L, 52T

A conceptual approach for students with a serious interest in mathematics. Geometric and physical intuition are emphasized but some attention is also given to the theoretical foundations of calculus. Material covers the basic concepts of calculus: limits and continuity, the mean value and inverse function theorems, the integral, the fundamental theorem, elementary transcendental functions, Taylor's theorem, sequence and series, uniform convergence and power series.
Exclusions: MAT133Y, 134Y, 135Y, 137Y
Prerequisite: Calc + A&G/FM

MAT223H
Linear Algebra I 39L

Matrices, linear systems, elementary matrices and the inverse of a matrix. Vector spaces over R, subspaces, basis and dimension. Real inner product spaces, geometry in Rn, lines and hyperplanes. Linear transformation, kernel, range, matrix representation, isomorphisms. The determinant, Cramer's rule, the adjoint matrix. Eigenvalues, eigenvectors, similarity, diagonalization. Projections, Gram-Schmidt process, orthogonal transformations and orthogonal diagonalization, isometries, quadratic forms, conics, quadric surfaces.
Exclusion: MAT240H
Prerequisite: (Calc + A&G)/MAT133Y/134Y/135Y/137Y
Prerequisite: MAT223H/240H

MAT239Y
Multivariable Calculus 78L

Sequences and series. Uniform convergence. Convergence of integrals. Elements of topology in R^2 and R^3. Differential and integral calculus of vector valued functions of a vector variable, with emphasis on vectors in two and three dimensional euclidean space. Extremal problems, Lagrange multipliers, line and surface integrals, vector analysis, Stokes' theorem, Fourier series, calculus of variations.
Exclusion: MAT235Y, 239Y, 257Y
Prerequisite: MAT134Y(80%)/135Y(80%)/137Y/157Y

MAT244H
Ordinary Differential Equations 39L

Ordinary differential equations of the first and second order, existence and uniqueness; solutions by series and integrals; linear systems of first order; non-linear equations; difference equations.
Exclusion: MAT267H
Prerequisite: MAT134Y/135Y/137Y/157Y, 223H/240H
Co-requisite: MAT235Y/237Y/239Y

MAT334H
Complex Variables 39L

Theory of functions of one complex variable, analytic and meromorphic functions. Cauchy's theorem, residue calculus, conformal mappings, introduction to analytic continuation and harmonic functions.
Exclusion: MAT357Y
Prerequisite: MAT235Y/237Y/239Y/257Y

APM346H
Differential Equations 39L

Sturm-Liouville problems, Green's functions, special functions (Bessel, Legendre), partial differential equations of second order, separation of variables, integral equations, Fourier transtorm, stationary phase method.
Prerequisite: MAT237Y/239Y/257Y

Other Course Descriptions

CHM 1**
General-Anal. Chemistry

Chemical bonding; structures of molecules; aspects of thermodynamics and and reaction dynamics; spectroscopy; cheistry of inorganic and organic compounds; introduction to classical and insrumental analytical chemistry; scope of analytical chemistry; signal response, sensitivity and limit-of-detection of various techniues. Solution equilibrium applications: gravimetry, titrimetry, acid-base, edox and copmlexometric processes.

AST121H
Origin and Evolution of the Universe 26L

The origin of the Universe, the origin of the chemical elements, the origin of stars and galaxies, the origin of life in the Universe. This course is intended for students who are enrolling in science courses.
Exclusion: AST101H, 201H, 220H
Prerequisite: OAC in Physics and Algebra and Geometry/Calculus

CSC108H
Introduction to Computer Programming 26L, 13T

Structure of computers; the computing environment. Programming in a high-level language such as Turing. Fundamental constructs: if statements, loops. Operations on strings and numbers. Data and program structuring using arrays and subprograms. Applications including sorting. Further topics chosen from recursion, record structures, other languages.
Exclusion: CSC139H, 148H, 149H, 150H
Prerequisite: Grade 12 Mathematics

FSL121Y
Intermediate French 78L, 26P

Written and spoken French, reinforcing oral/aural competence, reading comprehension, and writing skills.
Exclusion: OAC French. Not open to native or fluent speakers of French
Prerequisite: FSL102H, or some background in secondary school French or permission of Department

SPA100Y
Spanish Language for Beginners 26L, 26P, 26T

A comprehensive introduction to Spanish grammar, including a weekly laboratory hour, oral practice in small groups, and selected readings.
Exclusion: OAC Spanish or equivalent knowledge of Spanish This is a Language course

HIS242H
Europe in the Contemporary Era 26L, 13T

The evolution of European politics, culture, and society from 1914: the two world wars, Fascism and Nazism, the post-1945 reconstruction and the movement towards European integration.
Exclusion: HIS249Y

PHL/PHI245H Modern Symbolic Logic 39L
The application of symbolic techniques to the assessment of arguments. Propositional calculus and quantification theory. Logical concepts, techniques of natural deduction.


Stephen L. Dancs, Hon B Sc
Toronto, Canada, Tel./Fax: +1 (416) 963-9624
Comments to author: bf154@torfree.net

All contents copyright (C) 1996, Stephen L. Dancs. All rights reserved.
Revised: July 23, 1996
URL: http//:www.ncf.carleton.ca/~bv561/cdt.html