2011-2012 Undergraduate Calendar-Physics

Last updated: April 3, 2013 @ 11:43AM

Physics

Chair
Edward Sternin

Professors Emeriti
John E. Black, Ramesh C. Shukla

Professors
Shyamal K. Bose, Douglas H. Bruce, Bozidar Mitrovic, Fereidoon S. Razavi, Maureen Reedyk, Stuart M. Rothstein, Kirill Samokhin, Art van der Est

Associate Professors
David A. Crandles, Thad A. Harroun, Edward Sternin

Participating Faculty
Stephen Anco, Henryk Fuks, Alexander Odesskii, Jan Vrbik

Adjunct Professors
James A. Blackburn, John Katsaras, Reinhard Kremer, Gerald Moran, Ole Steuernagel

Academic Advisers
David Crandles, Maureen Reedyk

Senior Laboratory Instructor
Frank A. Benko

Laboratory Demonstrator
Fulvio Boseglav

Director Co-operative Programs
Cindy Dunne

General Information

Administrative Assistant
Elizabeth Horvath

905-688-5550, extension 3412
Mackenzie Chown B210
physics.brocku.ca

The department offers four-year programs of study leading to a Bachelor of Science (BSc) Honours in Physics, a BSc Honours Co-op option in Physics, a BSc with Major Physics and a three-year BSc Pass degree program. Students may take a single major in Physics or a combined major with Biological Sciences, Chemistry, Computer Science, Mathematics or Great Books/Liberal Studies.

In addition, the department offers a four-year Honours program leading to a BSc degree in Physics with a concentration in Applied Optics and Laser Technology. This program combines Brock courses with those offered by Niagara College.

The core of the program is designed to provide an understanding of the principles and fundamental interactions of classical and quantum physics as well as many applications of these principles in technology and everyday life. It is possible for non-Physics degree students to take advanced courses, provided they have the physics and mathematics required in the year 1 Physics program. An experimental physics path of PHYS 2P31 and 3P92 or a modern physics path of PHYS 2P50 and 3P91 are possible.

The Physics Co-op program combines academic and work terms over a four and one-half year period. Students spend two years in an academic setting, where they acquire the necessary background prior to taking the first work placement. In addition to the current fees for courses in academic study terms, Physics Co-op students are assessed an annual administrative fee (see the Schedule of Fees).

Eligibility to continue is based on the student's major average and non-major average. A student with a minimum 70 percent major average and a minimum 60 percent non-major average will be permitted to continue. A student with a major average lower than 70 percent will not be permitted to continue in the Physics Co-op program, but may continue in the Physics stream.

The Physics Co-op program designation will be awarded to those students who have honours standing and who have successfully completed a minimum of twelve months of Co-op work experience.

The department also offers a Minor in Physics program. The goal of this program is to introduce students to the fundamental concepts of various branches of physics and their applications. The selection of courses is tailored to the needs and interests of individual students with diverse backgrounds (e.g., philosophy, classics, business and finance, mathematics and other science programs). Students should consult one of the Undergraduate Student Advisers of the Physics Department (physics@brocku.ca or ext. 3412) to plan the sequence of courses most suited to their background and needs.

Program Notes

Students should consult a faculty adviser when planning years 3 and 4 of the BSc programs or year 3 of the BSc Pass program.
In 20 credit degree programs a maximum of eight credits may be numbered 1(alpha)00 to 1(alpha)99; at least three credits must be numbered 2(alpha)90 or above; at least three credits must be numbered 3(alpha)90 or above; and the remaining credits must be numbered 2(alpha)00 or above.
In 15 credit degree program a maximum of eight credits may be numbered 1(alpha)00 to 1(alpha)99; at least three credits must be numbered 2(alpha)90 or above; and the remaining credits must be numbered 2(alpha)00 or above.
In some circumstances, in order to meet university degree and program requirements, more than 15 or 20 credits may be taken.

Honours Program

Year 1

·	PHYS 1P21 or 1P91 (recommended)
·	PHYS 1P22 or 1P92 (recommended)
·	PHYS 1P23 or 1P93 (recommended)
·	CHEM 1F92
·	MATH 1P01 and 1P02, or MATH 1P05 and 1P06 (recommended)
·	MATH 1P12
·	one Humanities context credit or Social Sciences context credit

Year 2

·	PHYS 2P20, 2P31, 2P50 and 2P51
·	MATH 2F05, or MATH 2P03 and 2P08
·	MATH 2P12
·	the Humanities context credit or Social Sciences context credit not taken in year 1
·	one-half elective credit (see program note 2)

Year 3

·	PHYS 3P35, 3P36, 3P41, 3P70 and 3P91
·	MATH 3P08 and 3P09
·	one and one-half elective credits (see program note 2)

Year 4

·	PHYS 4P41 and 4P51
·	MATH 3P04
·	two credits from PHYS 3P90, 3P92, 3P93, 4F90, 4F91, 4P09, 4P61, 4P62, 4P64, 4P70, 4P71, 4P92, 4P94
·	one and one-half elective credits (see program note 2)

Physics Co-op (Honours only)

Students admitted to the Co-op program must follow the program schedule as listed below. Failure to adhere to the schedule may result in removal from the Physics Co-op program.

Year 1

·	PHYS 1P21 or 1P91 (recommended)
·	PHYS 1P22 or 1P92 (recommended)
·	PHYS 1P23 or 1P93 (recommended)
·	CHEM 1F92
·	MATH 1P01 and 1P02, or MATH 1P05 and 1P06 (recommended)
·	MATH 1P12
·	one Humanities context credit or Social Sciences context credit

Year 2

·	PHYS 2P20, 2P31, 2P50 and 2P51
·	MATH 2F05, or MATH 2P03 and 2P08
·	MATH 2P12
·	SCIE 0N90
·	the Humanities context credit or Social Sciences context credit not taken in year 1
·	one-half elective credit (see program note 2)

Spring/Summer Sessions:

·	PHYS 0N01 or 2C01

Year 3
Fall Term:

·	PHYS 3P35, 3P70 and 3P91
·	MATH 3P08
·	one-half elective credit

Winter Term:

·	PHYS 0N02 and 2C02

Year 4
Fall Term:

·	PHYS 0N03 and 2C03

Winter Term:

·	PHYS 3P36 and 3P41
·	MATH 3P09
·	one elective credit (see program note 2)

Spring/Summer Sessions:

·	PHYS 4F90 and 4F91
·	one-half elective credit

Year 5
Fall Term:

·	PHYS 3P92 or one-half elective credit
·	one credit from PHYS 4P30, 4P41, 4P52, 4P61, 4P64, 4P70, 4P94
·	PHYS 4P51
·	one half elective credit

BSc with Major Program

Year 1

·	PHYS 1P21 or 1P91 (recommended)
·	PHYS 1P22 or 1P92 (recommended)
·	PHYS 1P23 or 1P93 (recommended)
·	CHEM 1F92
·	MATH 1P01 and 1P02, or MATH 1P05 and 1P06 (recommended)
·	MATH 1P12
·	one Humanities context credit or Social Sciences context credit

Year 2

·	PHYS 2P20, 2P31, 2P50 and 2P51
·	MATH 2F05, or MATH 2P03 and 2P08
·	MATH 2P12
·	the Humanities context credit or Social Sciences context credit not taken in year 1
·	one-half elective credit (see program note 2)

Year 3

·	PHYS 3P35, 3P36, 3P41, 3P70 and 3P91
·	MATH 3P08 and 3P09
·	one and one-half elective credits (see program note 2)

Year 4

·	One of PHYS 3P90, 3P92, 3P93
·	one and one-half credits from PHYS 4P09, 4P41, 4P51, 4P61, 4P62, 4P64, 4P70, 4P71 and 4P94
·	two PHYS credits numbered 2(alpha)00 or above
·	one elective credit (see program note 2)

Pass Program

Satisfactory completion of the first three years of the Honours program entitles a student to apply for a Pass degree.

Concurrent BSc/BEd

The Department of Physics and the Faculty of Education co-operate in offering two Concurrent BSc (Honours)/BEd programs. The Physics BSc (Honours)/BEd programs combines the BA Honours program or BA Integrated Studies Honours program with the teacher education program for students interested in teaching at the Intermediate/Senior level (grades 7-12) and at the Junior/Intermediate level (grades 4-10). Refer to the Education-Concurrent BSc (Honours)/BEd (Intermediate/Senior) or Education-Concurrent BSc Integrated Studies (Honours)/BEd (Junior/Intermediate) program listings for further information.

Combined Major Program

Physics and Biological Sciences

Honours

Year 1

·	PHYS 1P21 or 1P91 (recommended)
·	one of PHYS 1P22, 1P23, 1P92, 1P93 (recommended)
·	BIOL 1F90
·	CHEM 1F92
·	MATH 1P01 and 1P02, or MATH 1P05 and 1P06 (recommended)
·	one Humanities context credit or one Social Sciences context credit

Year 2

·	PHYS 2P50 and 2P51
·	BIOL 2F01
·	one credit from BIOL 2P05, 2P92, 2P93, 2P96, 2P98, 2Q04
·	MATH 2F05, or MATH 2P03 and 2P08
·	the Humanities context credit or Social Sciences context credit not taken in year 1

Year 3

·	PHYS 2P31 and 3P02
·	one BIOL credit (see program note 2)
·	one and one-half BIOL credits numbered 2(alpha)00 to 3(alpha)99 or one and one-half PHYS credits numbered 2(alpha)00 to 3(alpha)99 (see program note 2)
·	one and one-half elective credits (see program note 2)

Year 4

·	One of PHYS 4F90 and 4F91, BIOL 4F90 and 4F91, PHYS 4F90 and one elective credit, BIOL 4F92 and one elective credit (see program note 2)
·	one PHYS credit numbered 2(alpha)90 or above (see program note 2)
·	one BIOL credit numbered 2(alpha)90 or above (see program note 2)
·	one credit from PHYS and/or BIOL courses numbered 2(alpha)90 or above (see program note 2)

Pass Program

Satisfactory completion of the first three years of the Honours program entitles a student to apply for a Pass degree.

Physics and Computer Science (Honours only)

Year 1

·	PHYS 1P21 or 1P91 (recommended)
·	one of PHYS 1P22, 1P23, 1P92 (recommended), 1P93
·	COSC 1P02 and 1P03
·	MATH 1P01 and 1P02, or MATH 1P05 and 1P06 (recommended)
·	MATH 1P66, and 1P67
·	one Social Sciences context credit

Year 2

·	PHYS 2P20, 2P31, 2P50 and 2P51
·	COSC 2P03 and 2P12
·	MATH 2F05, or MATH 2P03 and 2P08
·	one Humanities context credit

Year 3

·	Two credits from MATH 3P08, 3P09, PHYS 3P35, 3P36, 3P41, 3P70, 3P90
·	COSC 1P50, 2P13, 2P32 and 2P90
·	MATH 1P12
·	one-half elective credit

Year 4

·	Two credits from PHYS 4F90, 4P09, 4P41, 4P51, 4P61, 4P62, 4P64, 4P70, 4P92, 4P94
·	COSC 3F00
·	two COSC credits numbered 3(alpha)90 or above

Physics and Mathematics (Honours only)

Year 1

·	PHYS 1P21 or 1P91 (recommended)
·	one of PHYS 1P22, 1P23, 1P92 (recommended), 1P93
·	MATH 1P01 and 1P02, or MATH 1P05 and 1P06 (recommended)
·	MATH 1P12, and 1P40
·	one Humanities context credit
·	one Social Sciences context credit

Year 2

·	PHYS 2P20, 2P31, 2P50 and 2P51
·	MATH 2P12, 2P81 and 2P82
·	MATH 2F05, or MATH 2P03 and 2P08
·	one-half elective credit

Year 3

·	Two credits from PHYS 3P35, 3P36, 3P41, 3P70, 3P90
·	MATH 2F40, 3P08 and 3P09
·	one elective credit

Year 4

·	PHYS 4F90 and 4F91 or MATH 3P12 and one and one-half MATH credits numbered 3(alpha)90 or above
·	PHYS 4P51
·	one credit from PHYS 4P41, 4P61, 4P62, 4P64, 4P70, 4P94
·	MATH 3P04
·	one elective credit

Physics and Chemistry
Consult the Chemistry entry for a listing of program requirements.

Physics and Liberal Arts (Honours only)
Consult the Liberal Arts entry for listing of program requirements.

Minor in Physics

Students in other disciplines can obtain a Minor in Physics within their degree programs by completing four full credits from the following courses with a minimum 60 percent average:

·	PHYS 1P21 or 1P91
·	one of PHYS 1P22, 1P23, 1P92, 1P93
·	one-half additional PHYS credit
·	two and one-half credits from ASTR 1P01, 1P02 or PHYS credits numbered 2(alpha)00 or above

Brock/Colleges Articulation Agreement

Concentration in Applied Optics and Laser Technology

The concentration in Applied Optics and Laser Technology combines a basic Bachelor's education in the core fields within Physics with practical training in fibre optics, photonics, and high vacuum and laser technologies. This is a four-year honours program and involves courses offered through Brock University and Niagara College's postgraduate certificate program in Advanced Laser Technologies. Students completing the program will receive a B.Sc. Honours degree in Physics with concentration in Applied Optics and Laser Technology, as well as a postgraduate certificate in Advanced Laser Technologies from Niagara College.

The program aims to fulfill the increasing demand from the fibre optics and telecommunications industry for graduates with knowledge and technical skills in photonics, opto-electronic devices, and laser, thin film and high vacuum technologies. Normally, to acquire these qualifications students would first complete a university degree and then complete a suitable technical program at a college. The Brock-Niagara program combines the two in a single integrated package.

Students may enter this program directly in year one, or transfer to this program in or at the end of year 2 of any four-year Physics program. Enrolment will be limited, depending on the availability of lab space at Niagara College. Admission to the Concentration program will include concurrent admission to the Niagara College postgraduate certificate program in Advanced Laser Technology.

Honours-Niagara College

Year 1

·	PHYS 1P21 or 1P91 (recommended)
·	one of PHYS 1P22, 1P23, 1P92 (recommended), 1P93
·	CHEM 1F92
·	MATH 1P01 and 1P02, or MATH 1P05 and 1P06 (recommended)
·	MATH 1P12 and 1P98
·	one Humanities context credit or Social Sciences context credit

Year 2

·	PHYS 2P20, 2P31, 2P32, 2P50 and 2P51
·	MATH 2F05, or MATH 2P03 and 2P08
·	the Humanities context credit or Social Sciences context credit not taken in year 1
·	one-half elective credit

Year 3

·	taken at Niagara College

Year 4

·	PHYS 3P35, 3P36, 3P41 and 3P70
·	one PHYS credit numbered 3(alpha)90 or above
·	MATH 3P08
·	one and one-half elective credits

Master of Science (MSc) Program

The department offers an MSc program in condensed matter physics including experimental and/or theoretical research. Current research interests and activities involve experimental, theoretical and computational studies in materials science and condensed matter.

For details, see the Graduate Calendar or contact the Chair of the Department.

Course Descriptions

Note that not all courses are offered in every session. Refer to the applicable term timetable for details.

# Indicates a cross listed course
* Indicates primary offering of a cross listed course

Prerequisites and Restrictions

Students must check to ensure that prerequisites are met. Students may be deregistered, at the request of the instructor, from any course for which prerequisites and/or restrictions have not been met.

ASTRONOMY COURSES

ASTR 1P01
Introduction to Astronomy I
Description of the appearance of the night sky, history of astronomy, light and telescopes, measuring the properties of stars, structure and functioning of the Sun.
Lectures, 3 hours per week.
Completion of this course will replace previously assigned grade and credit obtained in ASTR 1F00.

ASTR 1P02
Introduction to Astronomy II
Formation and evolution of stars, properties of some unusual astronomical objects, such as pulsars and black holes, galaxies, cosmology and a discussion of the planets of the solar system.
Lectures, 3 hours per week.
Note: ASTR 1P01 is highly recommended.
Completion of this course will replace previously assigned grade and credit obtained in ASTR 1F00.

PHYSICS COURSES

PHYS 1P21
Mechanics and Waves
Kinematics, Newton's laws and their applications to equilibrium and dynamics with examples from biomechanics; special relativity.
Lectures, 3 hours per week; tutorial, 1 hour per week.
Note: students may not concurrently register in PHYS 1P91.
Completion of this course will replace previously assigned grade and credit obtained in PHYS 1P91.

PHYS 1P22
Electromagnetism, Optics and Modern Physics
Charges and fields, electric currents and circuits, electromagnetic waves and wave nature of light, elements of modern physics.
Lectures, 3 hours per week; tutorial, 1 hour per week.
Prerequisite(s): PHYS 1P21 or permission of the instructor.
Note: students may not concurrently register in PHYS 1P92.
Completion of this course will replace previously assigned grade and credit obtained in PHYS 1P92.

PHYS 1P23
Fluids, Heat, Light and Sound
Fluids in equilibrium, surface tension and capillary action; fluids in motion, viscosity and turbulent flow. Heat and temperature, elements of kinetic theory and the laws of thermodynamics. Geometrical optics, waves and sound.
Lectures, 3 hours per week; tutorial, 1 hour per week.
Note: students may not concurrently register in PHYS 1P93.
Completion of this course will replace previously assigned grade and credit obtained in PHYS 1P93.

PHYS 1P91
Mechanics and Waves with Laboratory
Combination of lectures and tutorials in PHYS 1P21 with a laboratory session.
Lectures, 3 hours per week; tutorial, 1 hour per week; lab, alternating weeks, 3 hours per week.
Note: students may not concurrently register in PHYS 1P21.
Completion of this course will replace previously assigned grade and credit obtained in PHYS 1P21.

PHYS 1P92
Electromagnetism, Optics and Modern Physics with Laboratory
Combination of lectures and tutorials in PHYS 1P22 with a laboratory session.
Lectures, 3 hours per week; tutorial, 1 hour per week; lab, alternating weeks, 3 hours per week.
Prerequisite(s): PHYS 1P91 or permission of the instructor.
Note: students may not concurrently register in PHYS 1P22.
Completion of this course will replace previously assigned grade and credit obtained in PHYS 1P22.

PHYS 1P93
Fluids, Heat, Light and Sound With Laboratory
Combination of lectures and tutorials in PHYS 1P23 with a laboratory session.
Lectures, 3 hours per week; tutorial, 1 hour per week; lab, alternating weeks, 3 hours per week.
Note: students may not concurrently register in PHYS 1P23.
Completion of this course will replace previously assigned grade and credit obtained in PHYS 1P23.

PHYS 2P02
Introduction to Medical Physics
Physical and chemical interactions of ionizing radiations and their biological effects, structural imaging (magnetic resonance imaging, ultrasound, computed tomography and optical microscopy); nuclear medicine, therapeutic applications of radiation.
Lectures, 3 hours per week; tutorial, 1 hour per week.
Prerequisite(s): one of 4U/M PHYS (SPH4U), PHYS 1P22, 1P23, 1P92, 1P93.

PHYS 2P20
Introductory Mechanics
Mechanics of particles and systems of particles by the Newtonian method; conservation of linear momentum, angular momentum and energy; elementary dynamics of rigid bodies; oscillators; motion under central forces; selected applications.
Lectures, problem sessions, 3 hours per week; lab, tutorial, 3 hours per week.
Prerequisite(s): PHYS 1P21 or 1P91 (recommended); one of PHYS 1P22, 1P23, 1P92 (recommended), 1P93; MATH 1P01 and 1P02.

PHYS 2P31
Analog Electronics
Conduction in metals and semi-conductors; circuit analysis; semi-conductor junction, diode and transistor; rectification, switching and amplification; operational amplifiers, active filters; laboratory instruments.
Lectures, lab, 6 hours per week.
Prerequisite(s): PHYS 1P21 or 1P91 (recommended); one of PHYS 1P22, 1P23, 1P92 (recommended), 1P93; one MATH credit or permission of the instructor.
Note: no previous course in electricity/magnetism/electronics is required. Secondary school algebra and some basic calculus will be used in the quantitative sections.

PHYS 2P32
Digital Electronics
Principles of digital electronics; combinatorial logic and circuits; sequential circuits, counters; digital computing and control; analog-to-digital conversion; signal sampling; elements of computational science; an introduction to programming.
Lectures, lab, 6 hours per week.
Prerequisite(s): PHYS 1P21 or 1P91 (recommended); one of PHYS 1P22, 1P23, 1P92 (recommended), 1P93; one MATH credit or permission of the instructor.

PHYS 2P50
Modern Physics
Special relativity, photons, the wave-particle aspects of electromagnetic radiation and matter; introduction to wave mechanics; the hydrogen atom and atomic line spectra; orbital and spin angular momenta; lasers.
Lectures, tutorial, 4 hours per week.
Prerequisite(s): PHYS 1P21 or 1P91 (recommended); one of PHYS 1P22, 1P23, 1P92 (recommended), 1P93; MATH 1P01 and 1P02.

PHYS 2P51
Introduction to Classical and Modern Optics
Geometrical and wave optics, reflection, refraction, lenses, matrix methods, aberrations, gradient index phenomena including fibre optics, interference, coherence, holography, Fraunhofer and Fresnel diffraction, polarization.
Lectures, lab, 6 hours per week.
Prerequisite(s): PHYS 1P21 or 1P91 (recommended); one of PHYS 1P22, 1P23, 1P92 (recommended), 1P93; MATH 1P01 and 1P02.

PHYS 3P02
Cellular Biophysics
Introduction to the molecular biophysics of cellular membranes, structure and function of the major cell components (lipids, proteins and carbohydrates), experimental physical techniques, photobiology, biological electrokinetics, bioinformatics, biomechanics, and biomimetics.
Lectures, 3 hours per week; lab, alternate week, 4 hours per week.
Prerequisite(s): PHYS 1P21 or 1P91 (recommended); one of PHYS 1P22, 1P23, 1P92, 1P93 (recommended) or permission of the instructor.

PHYS 3P35
Electromagnetism I
Electric field, divergence and curl of electrostatic field; relation between electric work and energy; conductors; application of Laplace's and Poisson's equation in electrostatics; electrostatic field in matter; field in polarized object and linear dielectric.
Lectures, 3 hours per week.
Prerequisite(s): MATH 2F05, or MATH 2P03 and 2P08.

PHYS 3P36
Electromagnetism II
Magnetostatics, divergence and curl of magnetic field; magnetic vector potential; magnetic field in matter; magnetization; field of magnetic object; magnetic field inside of linear and non-linear media; electrodynamics; Ohm's law; Faraday's law and Maxwell equations; energy and momentum in electrodynamics; electromagnetic waves.
Lectures, 3 hours per week.
Prerequisite(s): PHYS 3P35.

PHYS 3P41
Statistical Physics I
Introduction to probability distribution functions, accessible states, entropy, temperature, partition functions and relations to thermodynamic functions.
Lectures, 3 hours per week; tutorial, 1 hour per week.
Prerequisite(s): PHYS 2P50.

PHYS 3P70
Introduction to Quantum Mechanics
Wave particle dualism, Schrodinger equation, solution of simple one-dimensional barrier problems and the harmonic oscillator, hydrogen atom, angular momentum theory, introduction to perturbation theory and variational methods.
Lectures, lab/problem sessions, 4 hours per week.
Prerequisite(s): PHYS 2P50; MATH 2F05, or MATH 2P03 and 2P08.

PHYS 3P90
Classical Mechanics
Advanced treatment of the mechanics of particles and of rigid bodies; Lagrangian and Hamiltonian methods; Poisson brackets, applications to the theory of small oscillators and central force motions, elements of chaotic motions.
Lectures, 3 hours per week.
Prerequisite(s): PHYS 2P20; MATH 2F05, or MATH 2P03 and 2P08.
Completion of this course will replace previously assigned grade and credit obtained in PHYS 3P20.

PHYS 3P91
Experimental Physics I
Laboratory experiments to be selected from atomic physics, nuclear physics, solid state physics.
Lab, 1 day per week.
Prerequisite(s): PHYS 2P50 or permission of the instructor.

PHYS 3P92
Experimental Physics (Electronics) II
Operational amplifiers, converters, switches, microcomputers and their application to physical measurements.
Lab, 1 day per week.
Prerequisite(s): PHYS 2P31 or permission of the instructor.
Note: PHYS 2P32 recommended.

PHYS 3P93
Solid-State Devices
Principles of operation of solid-state devices, from the point of view of the quantum theory; electronic bands and conduction in semiconductors; operation and manufacture of silicon and germanium diodes, junction and field effect transistors; thin-film deposition technology; special topics.
Lectures, lab, 6 hours per week.
Prerequisite(s): PHYS 3P70.

PHYS 4F90
Research Project I
Small experimental, theoretical or applied physics research project to be carried out under the supervision of a member of the department.
Restriction: open to PHYS (single or combined) and CAST majors with either a minimum of 14.0 overall credits, a minimum 70 percent major average and a minimum 60 percent non-major average or approval to year 4 (honours).
Note: the project may, under special circumstances, be started in the summer months. Students must consult with the Department Chair regarding their proposed program during the first week of lectures.

PHYS 4F91
Research Project II
Detailed experimental, theoretical or applied physics research project to be carried out under the supervision of a member of the department.
Restriction: open to PHYS (single or combined) majors with either a minimum of 14.0 overall credits, a minimum 70 percent major average and a minimum 60 percent non-major average or approval to year 4 (honours) and permission of the Department.
Prerequisite(s): PHYS 4F90.
Note: the project may, under special circumstances, be started in the summer months. Students must consult with the Department Chair regarding their proposed program during the first week of lectures. PHYS 4F90 and 4F91 may be taken concurrently.

PHYS 4P09
Solitons and Nonlinear Wave Equations
(also offered as MATH 4P09)
Introduction to solitons. Travelling waves, nonlinear wave equations and evolution equations (Korteweg de Vries, Bousinesq, nonlinear Schrodinger, sine-Gordon). Soliton solutions and their interaction properties, Lax pairs, and construction of single and multisoliton solutions.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): one of MATH 3P09, 3P51, 3P52.

PHYS 4P30
Electromagnetic Waves
Electromagnetic wave propagation in vacuum, dielectrics, conductors and ionized gases; reflection, refraction, polarization at the plane boundary between two media; wave guide and transmission line propagation; dipole and quadrupole radiation fields; antenna systems; electromagnetic radiation pressure; transformation of the electromagnetic fields.
Lectures, problem sessions, 3 hours per week.
Prerequisite(s): PHYS 3P35, 3P36, MATH 3P08 and 3P09.

PHYS 4P41
Statistical Physics II
Fundamental postulates, equilibrium statistical mechanics and its relation to thermodynamics. Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics are derived and applied in appropriate physical situations of non-interacting and interacting particles; fluctuations; elementary treatment of transport theory.
Lectures, 3 hours per week; tutorial, 1 hour per week.
Prerequisite(s): PHYS 3P41, 3P70, MATH 3P08 and 3P09.

PHYS 4P51
Quantum Mechanics I
Postulates about states, observables, probabilities, change of state in a measurement, and time evolution. Dirac's bra and ket notation; representation and transformation theory. Two-level systems. Complete set of commuting observables and classification of states. Symmetries and their usage in classification of states.
Lectures, 3 hours per week.
Prerequisite(s): PHYS 3P70, MATH 3P08 and 3P09.

PHYS 4P52
Quantum Mechanics II
Operator methods in quantum mechanics, charged particles in electromagnetic field, angular momentum, variational method, time-independent and time-dependent perturbation theories, theory of scattering.
Lectures, 3 hours per week.
Prerequisite(s): PHYS 3P70, MATH 3P08 and 3P09.

PHYS 4P61
Nuclear Physics
Intrinsic properties of nuclei, nuclear binding energy; qualitative treatment of shell model; alpha, beta and gamma radioactivities, nuclear fission, characteristics of nuclear reactions.
Lectures, problem sessions, 3 hours per week.
Prerequisite(s): PHYS 2P50 and 3P70.

PHYS 4P62
Modern Wave Optics: Optical Tweezers to Atom Clouds
Optical lattices, spatial light modulators, evanescent waves and their applications from biology to ultracold atoms. Laser cooling and optical trapping. Manipulation of crystal properties by light. Optical patterns: tweezers, mirrors, funnels, bottles. Maple-based coursework.
Lectures, tutorial, 4 hours per week.
Prerequisite(s): PHYS 2P51 and MATH 2P03 or permission of the instructor.

PHYS 4P64
Introduction to Mathematical Physics
(also offered as MATH 4P64)
Calculus of variations, least action principle in physics, symmetries and conservation laws, differential-geometric structures (differential form, vector field, Riemannian metric). Applications to physics: electro-magnetic field as a one-form, gravity as a pseudo-Riemannian metric. Introduction to mathematical ideas of quantum mechanics.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 2F05, or MATH 2P03 and 2P08; MATH 2P12.

PHYS 4P70
Condensed Matter Physics I
Crystal structures and crystal binding; the vibration of atoms in solids and the thermodynamics of solids; introduction to transport properties of solids.
Lectures, 3 hours per week; tutorial, 1 hour per week.
Prerequisite(s): PHYS 3P41 and 3P70.

PHYS 4P71
Condensed Matter Physics II
Energy bands in metals and semiconductors, dynamics of electrons, Fermi surfaces and transport properties of solids, magnetism, screening in electron gas, optical properties.
Lectures, 3 hours per week; tutorial, 1 hour per week.
Prerequisite(s): PHYS 4P70.

PHYS 4P92
Advanced Electronics Laboratory
Families of logic devices, selection and implementation techniques; synchronous and asynchronous sequential circuits; safety and physical constraints; programmable array logic designs; digital signal processing, optoelectronics; CAD; circuit layout.
Lab, 1 day per week.
Prerequisite(s): PHYS 3P92.
Note: completion of a project from design to a working device is required.

PHYS 4P94
Relativity Theory and Black Holes
(also offered as MATH 4P94)
Review of Special Relativity and Minkowski space-time. Introduction to General Relativity theory; the space-time metric, geodesics, light cones, horizons, asymptotic flatness; energy-momentum of particles and light rays. Curvature and field equations. Static black holes (Schwarzschild metric), properties of light rays and particle orbits. Rotating black holes (Kerr metric).
Lectures, 3 hours; lab/tutorial, 1 hour per week.
Prerequisite(s): one of PHYS 2P20 and 2P50, MATH 2F05, MATH 2P03 and 2P08 or permission of the instructor.

PHYS 4V80-4V89
Special Topics
Examples of topics are relativity and cosmology; surface physics and electronic states in ordered and disordered systems.
Lectures, problem sessions, 4 hours per week.

CO-OP COURSES

PHYS 0N01
Co-op Work Placement I
First co-op placement (4 months) with an approved employer.
Restriction: open to PHYS Co-op students.

PHYS 0N02
Co-op Work Placement II
Second co-op placement (4 months) with an approved employer.
Restriction: open to PHYS Co-op students.

PHYS 0N03
Co-op Work Placement III
Third co-op placement (4 months) with an approved employer.
Restriction: open to PHYS Co-op students.

PHYS 0N04
Co-op Work Placement IV
Co-op placement (4 months) with an approved employer.
Restriction: open to PHYS Co-op students.

PHYS 0N05
Co-op Work Placement V
Co-op placement (4 months) with an approved employer.
Restriction: open to PHYS Co-op students.

PHYS 2C01
Co-op Reflective Learning and Integration I
Provide student with the opportunity to apply what they've learned in their academic studies through career-oriented work experiences at employer sites.
Restriction: open to PHYS Co-op students.
Prerequisite(s): SCIE 0N90.
Corequisite(s): PHYS 0N01.
Note: students will be required to prepare learning objectives, participate in a site visit, write a work term report and receive a successful work term performance evaluation.

PHYS 2C02
Co-op Reflective Learning and Integration II
Provide student with the opportunity to apply what they've learned in their academic studies through career-oriented work experiences at employer sites.
Restriction: open to PHYS Co-op students.
Prerequisite(s): SCIE 0N90.
Corequisite(s): PHYS 0N02.
Note: students will be required to prepare learning objectives, participate in a site visit, write a work term report and receive a successful work term performance evaluation.

PHYS 2C03
Co-op Reflective Learning and Integration III
Provide student with the opportunity to apply what they've learned in their academic studies through career-oriented work experiences at employer sites.
Restriction: open to PHYS C-op students.
Prerequisite(s): SCIE 0N90.
Corequisite(s): PHYS 0N03.
Note: students will be required to prepare learning objectives, participate in a site visit, write a work term report and receive a successful work term performance evaluation.

PHYS 2C04
Co-op Reflective Learning and Integration IV
Provide student with the opportunity to apply what they've learned in their academic studies through career-oriented work experiences at employer sites.
Restriction: open to PHYS Co-op students.
Prerequisite(s): SCIE 0N90.
Corequisite(s): PHYS 0N04.
Note: students will be required to prepare learning objectives, participate in a site visit, write a work term report and receive a successful work term performance evaluation.

PHYS 2C05
Co-op Reflective Learning and Integration V
Provide student with the opportunity to apply what they've learned in their academic studies through career-oriented work experiences at employer sites.
Restriction: open to PHYS Co-op students.
Prerequisite(s): SCIE 0N90.
Corequisite(s): PHYS 0N05.
Note: students will be required to prepare learning objectives, participate in a site visit, write a work term report and receive a successful work term performance evaluation.