Arts & Science Calendar 1998-99: Table of Contents: Programs and Courses
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PHY PHYSICS


On this page: Introduction | Faculty Members | Programs | Courses
See also: Course Summer Timetable | Course Winter Timetable | Secondary School Information | More on Department

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.

A program in physics has much to offer you. Besides traditional careers in teaching and research, knowledge of Physics is a powerful tool for a career in the Environmental or Life Sciences. An understanding of Physics is essential for those who are concerned about how society is affected by the impact of modern technology. The conceptual tools one acquires as a physicist can be applied to many occupations.

The Specialist Program offers an intensive preparation for a career in Physics. By choosing ones courses from the wide variety offered, one can emphasize experimental, theoretical or even applied sides of physics. In fourth year, students intending to undertake graduate studies are encouraged to take an Option or part of 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.

We have recently introduced a new program in Applied Physics which focuses more on subject matter which will help one in an industrial career. As part of this program, students are encouraged to take advantage of the Professional Experience Year program. The recently funded Nortel Applied Physics Laboratory is an integral part of the Applied Physics program.

The Professional Experience Year program ("PEY": see Study Elsewhere Program Options) 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. All students, most particularly those entering first year, are strongly urged to pick up a copy from the Department Office before term begins.

Associate Chair: Professor B. Statt, Room 324, McLennan Physical Laboratories (978-6674) (ugchair@physics.utoronto.ca)

Enquiries: Undergraduate Office, Room 301, McLennan Physical Laboratories (978-7057/5219)

Web Page: http://www.physics.utoronto.ca

Faculty Members

University Professors Emeriti
A.E. Litherland, B Sc, Ph D, FRSC, FRS
B.P. Stoicheff, OC, MA, Ph D, D Sc, FRSC, FRS

Professors Emeriti
R.E. Azuma, MA, Ph D A.D. May, MA, Ph D
H.C. Corben, MA, M Sc, Ph D K.G. McNeill, MA, D Phil, FI Nuc E (T)
R.M. Farquhar, MA, Ph D, FRSC (E) J.W. Moffat, Ph D, D Sc
E. Fawcett, MA, Ph D, F Inst P (U,S) D.A.L. Paul, BA, Ph D
G.D. Garland, OC, MA, Ph D, FRSC J.D. Prentice, M Sc, Ph D
G.M. Graham, M Sc, Ph D D.J. Rowe, MA, D Phil, FRSC
J.V. Iribarne, Dr In Chem J.C. Stryland, Ph D
D.G. Ivey, MA, Ph D L.E.H. Trainor, MA, Ph D
R. List, Dipl Phys ETH, Dr Sc Nat, FRSC G.F. West, MA, Ph D
F.D. Manchester, M Sc, Ph D T.S. Yoon, M Sc, Ph D

Professor and Acting Chair of the Department
P.K. Sinervo, B Sc, Ph D

Professor
and Associate Chair (Graduate Studies)
J.E. Sipe, M Sc, Ph D (T)

Associate Professor and Associate Chair
(Undergraduate Studies)
B.W. Statt, M Sc, Ph D

University Professors
W.R. Peltier, M Sc, Ph D, FRSC

Professors
R.C. Bailey, B Sc, Ph D A.W. Key, MA, D Phil (I)
† J.R. Bond, MS, PH D, FRSC J.D. King, BA, D Phil (S)

† M.J. Bronskill, M Sc, Ph D, FCCPM M.J.G. Lee, MA, Ph D (S)

H.R. Cho, M Sc, Ph D G.J. Luste, BA, Ph D
R.F. Code, AM, Ph D (E) † J.F. Martin, B Sc, D Phil
R.C. Desai, B Sc, Ph D R.J.D. Miller, R.J.D., B Sc, Ph D
T.E. Drake, M Sc, Ph D †K.H. Norwich, M Sc, MD, Ph D
J.R. Drummond, MA, D Phil P.J. O'Donnell, B Sc, Ph D (S)
D.J. Dunlop, MA, Ph D, FRSC (E) R.S. Orr, B Sc, Ph D
R.N. Edwards, B Sc, Ph D, C Phys, F Inst P J.M. Perz, MA Sc, Ph D (S)
A. Griffin, M Sc, Ph D (S) T.G. Shepherd, B Sc, Ph D
R. Holdom, MA, Ph D H.M. van Driel, M Sc, Ph D
A.E. Jacobs, M Sc, Ph D (S) M.B. Walker, B Eng, D Phil
S. John, B Sc, Ph D S.S.M. Wong, M Sc, Ph D (E)
† M.L.G. Joy, MA Sc, Ph D D. York, BA, D Phil, FRSC

Associate Professors
D.C. Bailey, B Sc, Ph D R.S. Marjoribanks, MS, Ph D
R.K. Logan, B Sc, Ph D (N) J.X. Mitrovica, M Sc, Ph D
G.W.K. Moore, B Sc, Ph D (E)

Assistant Professors
M. Luke, AM, Ph D K. Strong, B Sc, D Phil
S. Morris, M Sc, Ph D (E) B. Tolton, Ph D
A.M. Steinberg, MA, Ph D W. Trischuk, B Sc, Ph D

Senior Tutors
M. From, Ph D J.M. Pitre, M Sc, Ph D (SM)
D.M. Harrison, M Sc, Ph D S.M. Quick, M Sc, Ph D (S)
K. Hughes, M Sc, Ph D (E)

† Cross-appointed

PHYSICS PROGRAMS

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

APPLIED PHYSICS (Hon.B.Sc.)

Consult Professor B. Statt, Associate Chair (Undergraduate Studies), Department of Physics.

Specialist program: S10851 (13.5 full courses or their equivalent, including at least one 400-series course)
First Year: MAT 135Y/137Y, 223H; PHY 140Y
Second Year: MAT 235Y/237Y, 244H; PHY 225H, 251H, 252H, 255H, 256H
Third Year: APM 346H; MAT 334H; PHY 351H, 352H, 355H
Forth Year:
1. PHY 459H, 478H
2. In addition, students are required in their 3rd/4th year to take 2.0 courses in practical physics from:

PHY 305-308H; 405-408H; 325Y/326H; 425Y/426H; 495H/496H; and
3. an equivalent of 1.5 courses selected from one of the following streams:
Condensed Matter Physics and Quantum Optics: PHY 353H, 485H, 487H
Atmospheric Physics: PHY 315H, 497H, 498H, 499H
Geophysics: JGP 438H, PHY 492H, 493H, 494H

NOTE: Students intending to pursue a career in Industry are strongly urged to take advantage of the Professional Experience Year Program.

PHYSICS (B.Sc.)

Consult Professor B. Statt, Associate Chair (Undergraduate Studies), Department of Physics.

Specialist program (Hon.B.Sc.): 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
Forth 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/309H/407H/408H/409H

Major program Major program:

A. `CORE' MAJOR M19441 (7.5 full courses or their equivalent)
First Year: MAT 137Y, 223H; PHY 140Y
Second Year:
1. MAT 237Y, PHY 225H
2. Three of: PHY 251H, 252H, 255H, 256H
Third Year:
1. MAT 244H; PHY 305H/307H/308H/309H/326H
2. Two of: PHY 351H, 352H, 353H, 355H, 357H, 358H

B. `GENERAL' MAJOR M1925 (7 full courses or their equivalent)

NOTE: This program is intended for students in the Life Sciences
First Year: MAT 135Y/137Y; PHY 138Y/140Y
Second Year: MAT 235Y/237Y; PHY 225H, 238Y/(251H, 255H)
Third Year:
1. MAT 244H, PHY 256H, 305H/307H/308H/309H/326H
2. One full course equivalent from: JPA 310H, JGP 438H, PHY 315H, 346H, 445H

Minor program Minor program:

A. `CORE' MINOR R19441 (4 full courses or their equivalent)
First Year: PHY 140Y
Second Year:
1. PHY 225H
2. Three of: PHY 251H, 252H, 255H, 256H
Third Year:
1. PHY 305H/307H/308H/309H/326H
2. One of PHY 351H, 352H, 355H

B. `LIFE AND ENVIRONMENTAL' MINOR R25651 (4 full courses or their equivalent)
First Year: MAT 135Y/137Y; PHY 138Y/140Y
Second Year: ENV 235Y/JPU 200Y/PHY 238Y
Third Year: One full course equivalent from: BOT 323H; JPA 305H/310H; JGP 438H; PHY 315H, 346H

EARTH SYSTEMS: PHYSICS AND ENVIRONMENT — See DIVISION OF THE ENVIRONMENT

PHYSICS AND ASTRONOMY — See ASTRONOMY

PHYSICS AND BIOLOGY — See BIOLOGY

PHYSICS AND CHEMISTRY — See CHEMICAL PHYSICS

PHYSICS AND COMPUTER SCIENCE — See COMPUTER SCIENCE

PHYSICS AND GEOLOGY — See GEOLOGY

PHYSICS AND MATHEMATICS — See MATHEMATICS

PHYSICS COURSES

(see Section 4 for Key to Course Descriptions)

For Distribution Requirement purposes, all PHY courses are classified as SCIENCE courses.

NOTE Books listed in course descriptions will not necessarily be the texts for the course, but do indicate the level of presentation. Pre- and co-requisites are recommendations which may be waived in special circumstances - students should consult the Department prior to the beginning of term.

SCI199Y
First Year Seminar 52T

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 breadth requirement course; see First Year Seminars: 199Y.

PHY100H
The Magic of Physics 26L, 13T

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.
Exclusion: May not be taken in conjunction with any other PHY 100-series course

PHY100H
is primarily intended as a Science Distribution Requirement course for students in the Humanities and Social Sciences.

NOTE First Year Laboratory

Taken by all students enrolled in PHY110Y, 138Y, 140Y. An introductory course in experimentation, starting with selected experiments, 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.

PHY110Y
Basic Physics 78L, 39P, 26T

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 PHY100Y giving description of laboratory)

Reference: Cutnell, Physics (Wiley)
Exclusion: OAC Physics, PHY100H, 138Y, 140Y
Prerequisite: OAC Mathematics (OAC Calculus recommended)
Co-requisite: Students intending to take any higher level Physics course are expected to take at least MAT135Y PHY110Y can be taken as a Science course for Distribution Requirement purposes.

PHY138Y
Physics for the Life Sciences I 52L, 39P, 26T

This course is recommended strongly for students following a life science program. 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 PHY100Y giving description of laboratory)

Reference: Sternheim and Kane, General Physics (Second Edition; Wiley)
Exclusion: PHY100H, 110Y, 140Y
Prerequisite: OAC Calculus, OAC Physics
Co-requisite: MAT135Y/137Y/157Y PHY140Y
Foundations of Physics 78L, 39P, 26T

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 PHY100Y giving description of laboratory)
Exclusion: PHY100H/110Y/138Y
Prerequisite: OAC Calculus and OAC Physics
Co-requisite: MAT137Y/157Y, (MAT223H/240H recommended)

200-SERIES COURSES

NOTE All 200-series PHY courses require a 100-series MAT prerequisite. See co-requisite entries under 100-series PHY courses above.

JPU200Y
The Way of Physics 52L, 26T

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, curvature of space, quantum physics, chaos, quarks and big bang cosmology. 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.

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

ENV235Y
Physics and Chemistry of Planet Earth (see "ENV: Division of the Environment") 52L

The formation and evolution of Earth as a planet in the Solar System: origin of the elements, composition of planets, mantle-core differentiation, tectonics, geologic change and time scales. The biosphere: i.e., the Earth's atmosphere, oceans and crust: operation as a physicochemical system, atmospheric composition and roles of major and minor constituents, ocean/atmosphere energy budgets, circulations and couplings; climate, glaciation. The effects of human intervention and natural processes: e.g., groundwater quality, atmospheric change, volcanic activity. Given by the Departments of Physics and Chemistry.
Prerequisite: CHM135Y/137Y/150Y/157Y, MAT135Y/137Y/157Y/JMB170Y, PHY138Y/140Y

PHY238Y
Physics for the Life Sciences II 78L, 26T

Electromagnetism; biological effects of radiation; physical optics; macroscopic phenomena; heat engines and metabolism. Examples are taken, where applicable, from the life sciences.

Reference: Custom published booklets will be available for the various parts of the course.
Exclusion: PHY251H
Prerequisite: (PHY110Y, MAT135Y)/PHY138Y/140Y
Recommended preparation: BIO150Y/a CHM100-series course
Co-requisite: None, but students taking any higher level Physics course are expected to have at least MAT235Y

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 26L, 13T

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.
Prerequisite: PHY138Y/140Y
Co-requisite: MAT235Y/237Y/257Y, (MAT244H recommended)

PHY256H
Introduction to Quantum Physics 26L, 13T

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)

PHY299Y
Research Opportunity Program

Credit course for supervised participation in faculty research project. See Research Opportunity Program for details.

300-SERIES COURSES

NOTE Students taking 300-series courses are invited to attend the Thursday afternoon Department colloquia. Upon request, the Department of Physics provides staff advisers during the Spring Term for those taking 300-series courses.

JPA305H
Introduction to Archaeometry (formerly JPA300Y) 26L, 13P

Introduction to methods for remote sensing of buried archaeological remains, dating, and analysis of ancient materials. Application of methods and interpretation of results in archaeological contexts. (Offered in alternate years) (Given by the Departments of Physics and Anthropology)

Reference: Aitken, Physics and Archaeology; Tite, Methods of Physical Examination in Archaeology; Fleming, Dating in Archaeology

JPA310H
Physics and Archaeology (formerly JPA300Y) 26L, 13P

Introduction to the principles behind archaeometric methods for remote sensing, dating, and analysis of archaeological materials, and interpretation of results. Offered in conjunction with JPA305H. (Offered in alternate years) (Given by the Departments of Physics and Anthropology)
Prerequisite: Any 1st-year Physics course or permission of instructor
Co-requisite: JPA305H

PHY305H
Electronics Lab I 26L, 39P

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.
Prerequisite: PHY225H, 251H, 255H

NOTE Computational Laboratory

Students may select one or more modules from PHY307H/308H/309H below. The laboratory functions as an integrated lecture course/laboratory program.

PHY307H
Introduction to Computational Physics 13L, 39P

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.
Co-requisite: Any third-year lecture course in Physics

PHY308H
Times Series Analysis 13L, 39P

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.
Co-requisite: Any third-year lecture course in Physics

PHY309H
Quantum Methods Using Computer Algebra 13L, 39P

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.
Co-requisite: Any third-year lecture course in Physics

PHY315H
Radiation in Planetary Atmospheres 26L

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.
Prerequisite: PHY238Y/251H, MAT235Y/237Y

PHY325Y/326H
Modern Physics Laboratory 150P

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

PHY346H
Intermediate Biophysics 26L

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.
Prerequisite: MAT235Y/237Y/257Y, PHY238Y/251H

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

PHY355H
Quantum Mechanics I 26L, 13T

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.

Reference: Cohen-Tannoudji, Quantum Mechanics, Vol. 1, Wiley
Exclusion: CHM326H
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

PHY358H
Atoms, Molecules and Solids 26L, 13T

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.
Prerequisite: PHY355H

PHY371Y/372H
Supervised Reading in Physics TBA

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.
Prerequisite: Permission of Department

400-SERIES COURSES

NOTE A program including one or more of PHY 470-472, PHY 478-479, or PHY 480-498 must be endorsed by the Department. Students taking 400-series courses are invited to attend Thursday afternoon Department colloquia.

JPA400Y
Advanced Physics and Archaeology 156P

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. (Offered in alternate years) (Given by the Departments of Physics and Anthropology)
Prerequisite: JPA310H

PHY405H
Electronics Lab II 26L, 39P

The laboratory functions as an integrated lecture course/laboratory program.

Transistors, BJTs and MOSFETs: analysis tools, amplifier design. Digital devices: numbering systems, codes and representations, read-outs, decoders, registers, multiplexing, debouncing, state machines, memory, errors. Digitization, processing, aliasing. Microprocessors; busses, IO, data transmission, a/d and d/a. Active linear analogue circuits: response analysis, feedback, filters, oscillators, amplifiers, Fourier and Laplace transforms.
Prerequisite: PHY305H

PHY406H
Computer and Interface Systems Lab 26L, 39P

The laboratory functions as an integrated lecture course/laboratory program.

Computer as controller and data collector; programming and interface methodologies; the principles of analog-to-digital and digital-to-analog conversion; elementary data analysis; collection methodologies; simple data analysis concepts; signal processing techniques; implementation in modern laboratory environment, examples and experiments.
Prerequisite: PHY225H, 251H, 255H
Recommended preparation: PHY405H

NOTE Computational Laboratory

Students may select one or more modules from PHY407H/408H/409H below. The laboratory functions as an integrated lecture course/laboratory program.

PHY407H
Introduction to Computational Physics 13L, 39P

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.
Prerequisite: Any third-year lecture course in Physics

PHY408H
Times Series Analysis 13L, 39P

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.
Prerequisite: Any third-year lecture course in Physics

PHY409H
Quantum Methods Using Computer Algebra 13L, 39P

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.
Prerequisite: Any third-year lecture course in Physics

PHY425Y/426H
Advanced Modern Physics Laboratory 150P

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.
Prerequisite: PHY325Y/326H

JGP438H
Shallow Crust Geophysics 26L, 52P

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 geology students.
Prerequisite: GLG306H, PHY138Y/140Y or permission of instructor

PHY445H
Medical Imaging 26L, 20P, 13T

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.

Reference: E. Krestel, Imaging Systems for Medical Diagnostics, Siemans, 1990
Prerequisite: MAT244H/APM346H; MAT235Y/237Y; PHY238Y/251H
Recommended preparation: PHY307H/308H

PHY457H
Quantum Mechanics II 26L, 13T

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

PHY459H
Macroscopic Physics 26L, 13T

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.
Prerequisite: PHY252H, 351H

PHY460H
Nonlinear Physic 26L

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

PHY471Y/472H
Supervised Reading in Physics TBA

These self-study courses are similar to PHY371Y/372H, at a higher level.
Prerequisite: Permission of Department

PHY478H/479Y
Undergraduate Research Project TBA

An introduction to research in Physics. For further information contact the Associate Chair, Undergraduate Studies.
Prerequisite: Permission of Department

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.

The Advanced Courses

PHY480H
Basic Statistical Mechanics 26L

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.

PHY481H
Statistical Mechanics of Interacting Systems 26L

Topics include: thermodynamic fluctuations, distribution functions, interacting classical fluids, phase transitions, Ising model, mean field theory, scaling and universality.

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; 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.

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, geodesics, curvature tensor and Bianchi identities; variational principle and Einstein's gravitational field equations; gravitational waves.

PHY484H
Relativity Theory II 26L

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.

PHY485H
Modern Optics 26L

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.
Prerequisite: PHY353H, 355H

PHY486H
Photons and Atoms 26L

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.
Prerequisite: PHY352H, 353H, 355H, 452H, 480H

PHY487H
Condensed Matter Physics 26L

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.

PHY488H
Introduction to Particle Theory 26L

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.

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 include the standard electroweak model, scattering and parton distributions, strong interactions and quantum chromodynamics.
Prerequisite: PHY488H or an A grade level in PHY357H

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.

PHY491H
Current Interpretations of Quantum Mechanics 26L, 13T

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.
Prerequisite: PHY457H

PHY492H
Physics of the Earth 26L

Designed for students interested in the physics of the Earth and the planets but does not include geophysical prospecting. Provides a background for the study of the Earth as a unified dynamic system and includes topics related to: the determination of internal divisions in the planet; the age and thermal history of the planet; the Earth's gravitational field and the concept of isostasy; the development and evolution of the Earth's large scale surface features (plate tectonics, plate loading and flexure); mantle rheology; and geodetic measurement techniques.

PHY493H
Geophysical Imaging I 26L

This course covers wavefield and ray approximation methods for imaging the interior of the Earth using seismology.

PHY494H
Geophysical Imaging II 26L

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.

PHY495H
Experimental Global Geophysics 26L

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).

PHY496H
Experimental Applied Geophysics 39P

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.
Co-requisite: PHY493H/494H

PHY497H
Introduction to Atmosphere-Ocean Dynamics 26L

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.

PHY498H
Atmospheric Physics - Clouds 26L

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.

PHY499H
Earth Observations from Space 26L

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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Revised: April 6, 1998

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