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