## P H Y S I C S

### PHYS 00s

### PHYS 100s

Course ID: 007388

**Physics 1**

An introduction to physics for students intending to concentrate their further studies in biology, dentistry, medicine and paramedicine; includes particle kinematics and dynamics, energy and momentum conservation, and rotational mechanics. [Offered: F, W; also offered online: W]

*Antireq: PHYS 115, 121*

Course ID: 007390

**Physics 2**

A continuation of PHYS 111; includes simple harmonic motion, electrostatic force and potential, electric current and power, DC circuits, magnetic field and induction, wave motion, sound and optics. [Offered: W,S; also offered online: S]

*Prereq: PHYS 111 or 121;*

*Antireq: PHYS 122, 125*

Course ID: 007392

**Mechanics**

Brief review of kinematics. Particle dynamics, work, energy, conservation of energy. Conservation of linear momentum, collisions, rotational kinematics and dynamics, conservation of angular momentum. Equilibrium of rigid bodies. [Offered: F, W, S]

*Antireq: PHYS 111, 121; First year Engineering students only*

Course ID: 007393

**Mechanics**

An introductory course in physics for students intending to concentrate their future studies in the physical sciences, optometry, or mathematics; includes vectors (dot and cross products), particle kinematics and dynamics, forces in nature, work and energy, conservation of energy and linear momentum, rotational kinematics and dynamics, and conservation of angular momentum.

*[Note: Successful completion of 4U Calculus and Vectors, 4U Advanced Functions and 4U Physics is required. Offered: F, also offered online: W]*

*Coreq: One of MATH 104, 127, 137, 147.*

*Antireq: PHYS 111, 115, ECE 105*

Course ID: 013651

**Waves, Electricity and Magnetism**

Simple harmonic motion, resonance, damped harmonic motion, complex numbers, wave motion and sound, electrostatic force and potential, electric current and power, capacitors, DC circuits, LRC circuits, introduction to magnetic fields Lorentz Force. [Offered: W, S; also offered online: S]

*Prereq: One of PHYS 111 (minimum grade 70%), 115, 121, ECE 105.*

*Coreq: One of MATH 127, 137, 147.*

*Antireq: PHYS 112, 125*

Course ID: 013640

**Modern Physics**

An introductory course in modern physics; includes relativity, quantum physics, atomic physics, nuclear physics, particle physics and gravitation. [Offered: W]

*Prereq: One of PHYS 111 (minimum grade 70%), 115, 121, ECE 105.*

*Coreq: PHYS 112 or 122*

Course ID: 007398

**Physics for Engineers**

Oscillations; simple harmonic motion. Wave motion, travelling and standing waves; transverse and longitudinal waves, including sound. Geometrical optics; reflection and refraction. Physical optics; interference and diffraction. Quantum physics; quantization of radiation; hydrogen atom. [Offered: W,S]

*Prereq: PHYS 115; Engineering students only.*

*Antireq: PHYS 112, PHYS 122*

Course ID: 013959

**Introduction to the Universe**

A survey course in astrophysics intended for Physics and Astronomy students. Astrophysical processes, the sky, the Sun, stars, black holes, the Milky Way and other galaxies, Big Bang cosmology.

*[Note: students in Honours Physics and Astronomy programs must also take PHYS 175L; Offered: W]*

*Prereq: One of PHYS 111,115,121; one of MATH 116, 117, 127, 137,147.*

*Antireq: SCI 237, 238*

### PHYS 200s

Course ID: 013965

**Electricity and Magnetism for Life and Medical Physics**

Coulomb's law, electric field, Gauss' law, potential, current, resistance, electromotive force, D.C. circuits, magnetic fields, induced electromotive forces; applications include cell membrane potentials, action potentials, role of charge in structure and function of DNA, basis for the magneto-encephalogram and biomedical instrumentations. [Offered: F]

*Prereq: One of PHYS 112, 122; One of MATH 118, 119, 128, 138, 148.*

*Antireq: PHYS 242*

Course ID: 013968

**Modeling Life Physics**

Introduction to modeling living systems and their components. Statistical methods in data analysis, curve fitting, including p values. Fourier series and transforms, structural analysis, including nearest neighbor distributions in biomedical applications. Introduction to methods for analysis of transport properties in biological systems. Use of computers in these areas. [Offered: F]

*Prereq: One of PHYS 112, 122; One of MATH 116, 117, 127, 137, 147.*

*Coreq: One of MATH 118, 119, 128, 138, 148*

Course ID: 010361

**Measurement Laboratory**

A laboratory that teaches programming for the computer interfacing of physics experiments and automatic data collection.

*[Note: Lab alternate weeks. Offered: F].*

*Prereq: PHYS 122L; Honours Materials and Nanosciences and Honours Physics students only*

Course ID: 013969

**Introduction to Quantum Mechanics**

Introduction to quantization, wave-particle duality and the uncertainty principle The Schroedinger equation and solvable examples. Topics will include stationary states of particle-in-a-box, harmonic oscillator, and the hydrogen atom. Quantization of angular momentum and spin. Introduction to approximation methods including time-independent perturbation theory. Modern applications of quantum mechanics. [Offered: W]

*Prereq: One of PHYS 112, 125, 122, ECE 106; One of MATH 118 or 119, 128, 138, 148.*

*Coreq: One of MATH 212, 228, AMATH 250, 251.*

*Antireq: CHEM 356, NE 232, PHYS 234, ECE 405*

Course ID: 007407

**Quantum Physics 1**

Background of quantum physics. Introduction to formalism of quantum physics. Introduction to operators. Quantization, waves, and particles. The uncertainty principle. The Schroedinger equation for one-dimensional problems: bound states in square wells, harmonic oscillator, transmission through barriers.

*[Note: CS 114, PHYS 236, or knowledge of computational methods is recommended. Offered: W, S]*

*Prereq: PHYS 112 or 122; One of PHYS 249, MATH 114, 136; One of MATH 128, 138, 148.*

*Coreq: One of MATH 228, AMATH 250, AMATH 251.*

*Antireq: CHEM 356, NE 232, PHYS 233, ECE 405*

Course ID: 013643

**Electricity and Magnetism 1**

Electrostatics in vacuum, electric potential, conductors and currents, magnetostatics in vacuum, electromagnetic induction. [Offered: W,S]

*Prereq: One of PHYS 112,122; One of MATH 128, 138, 148; (MATH 227 or co-requisite: AMATH 231).*

*Coreq: PHYS 242L for science students except Mathematical Physics & Materials and Nanosciences plan.*

Course ID: 016205

**Computational Physics and Linear Algebra**

Computational techniques; numerical accuracy and speed; Python libraries and implementation; algorithms for numerical integration; matrix operations. Computational approach to vectors in 2- and 3-space; linear equations, matrices, determinants; eigenvalues and diagonalization. [Offered: F]

*Prereq: One of CS 114, 116, 136, 146*

Course ID: 007422

**Geometrical and Physical Optics**

Geometrical optics: image formation, ray tracing through multiple optical components, dispersion by prisms, optical fibers, optical instruments - eyes, telescopes, microscopes, and cameras, introduction to aberrations; physical optics: interference and interferometers, diffraction, imaging resolution, diffraction gratings and their use in spectroscopy; wave-particle duality; introduction to the electromagnetic nature of light and polarization. [Offered: F]

*Prereq: PHYS 112 or 122; One of MATH 108, 128, 138, 148.*

*Coreq: PHYS 256L for Science students except for Mathematical Physics Plan.*

*Antireq: ECE 404*

Course ID: 013118

**Intermediate Physics Laboratory**

Experiments in selected physics topics.

*[Note: Lab alternates weeks. Approximately a week before a particular lab is held, a one-hour lecture will be given on the material to be covered in the lab. Students in programs joint with Physics should see department for enrolment access. Offered: W,S]*

*Prereq: PHYS 232L or 256L; Honours Physics, Physics and Astronomy, or Materials and Nanosciences.*

*Coreq: PHYS 242*

Course ID: 003320

**Classical Mechanics and Special Relativity**

Newtonian dynamics of particles and systems of particles. Oscillations. Gravity and the central force problem. Lorentz transformations and relativistic dynamics. [Offered: W,S]

*Prereq: One of PHYS 112, 122; One of MATH 108, 128, 138, 148; One of MATH 228, AMATH 250, 251;*

*Antireq: AMATH 261, 271*

Course ID: 015985

**Probability, Statistics, and Data Analysis for Physics and Astronomy**

Probability, probability distributions, errors, descriptive statistics, statistical inference (hypothesis testing, fitting, confidence intervals), computational methods (e.g., Monte Carlo) in Python, examples from physics and astronomy. [Offered: W, S]

*Prereq: PHYS 122, MATH 227; One of PHYS 236 or CS 114, 116, 136, 146.*

*Antireq: STAT 230, 231*

Course ID: 012773

**Introduction to Biophysics**

Introduction to a physical understanding of biological systems at macro and molecular scales. The course is intended for second-year science and engineering students and will cover a broad spectrum of topics in biophysics, as well as an introduction to neurobiology, nanotechnology, and biotechnology. [Offered: W,S]

*Prereq: Level at least 2A Honours Science or Engineering plans*

*(Cross-listed with BIOL 280)*

### PHYS 300s

Course ID: 007434

**Quantum Physics 2**

Formalism of quantum mechanics. Operator approach to the harmonic oscillator. Quantum mechanics in three dimensions: Hydrogen atom, angular momentum and spin. Time-independent perturbation theory. Fine structure of hydrogen. Zeeman effect. Identical particles. The variational principle. Ground state of the helium atom. Applications in atomic and molecular physics. [Offered: W]

*Prereq: PHYS 234 or CHEM 356; One of MATH 228, AMATH 250, 251; MATH 227 or 237 or 247.*

*Antireq: AMATH 373*

Course ID: 012032

**Condensed Matter Physics**

Overview of condensed matter ordered and disordered systems. Thermodynamic origin of order and phase transitions. Waves. Properties of the solid state. Crystals and fractals. Overview of Fourier Series. Reciprocal lattice. Diffraction. Classical elastic theory of the crystalline state. Electrons in a periodic potential, Band structure and Fermi surface. [Offered: W]

*Prereq: PHYS 234 or CHEM 356; Level at least 3A Engineering, Mathematics or Science students*

Course ID: 013644

**Electricity and Magnetism 2**

Electric and magnetic fields in media, auxiliary fields, Maxwell's equations, electromagnetic waves, electric and magnetic properties of matter.

*[Note: PHYS 236 or knowledge of computational methods recommended. Offered: F,S]*

*Prereq: PHYS 242; One of MATH 228, AMATH 250, AMATH 251.*

Course ID: 016206

**Advanced Computational Physics**

Algorithms for solving differential equations; Monte Carlo techniques; Fourier transforms; programming and computational techniques using Python, applied to physical problems such as astrophysics, electricity and magnetism, classical and quantum mechanics; introduction to machine learning and artificial intelligence. [Offered: W]

*Prereq: PHYS 236 or PHYS 249; PHYS 234, PHYS 242, and (AMATH 271 or PHYS 263).*

*Antireq: PHYS 239*

Course ID: 007444

**Thermal Physics**

Temperature and thermodynamic equilibrium. Work, internal energy and heat; first law, with examples. Kinetic theory of gases. Basic probability theory. Microscopic states and entropy. Absolute temperature, reversibility and the second law. Thermodynamic Functions and Maxwell's relations. Phase transitions. Third Law. Other applications of thermodynamics. [Formerly PHYS 258. Offered: F, S]

*Prereq: PHYS 112 or 122; One of MATH 227, 237, 247; One of MATH 228, AMATH 250, 251.*

*Antireq: CHEM 254, ECE 403*

Course ID: 007445

**Statistical Mechanics**

Fundamental postulate of statistical thermodynamics. Entropy. Microcanonical, canonical, and grand canonical ensembles. Fermi-Dirac, Bose-Einstein, and Boltzmann Statistics. Maxwell-Boltzmann velocity distribution. Applications to specific heat of solids, classical and quantum gases, electrons in metals, Planck's law of radiation, and Bose-Einstein condensation. [Offered: W]

*Prereq: One of PHYS 358, ECE 403, CHEM 254, ME 250; One of PHYS 233, 234, CHEM 356, co-requisite: AMATH 373*

Course ID: 007446

**Modern Physics Laboratory 1**

Selected experiments in mechanics, optics, electronics, atomic, molecular, nuclear, and solid state physics.

*[Note: Students in programs joint with Physics should see department for enrolment access. Offered: F,W,S]*

*Prereq: One of MNS 201L, PHYS 260L, 270L; Honours Physics, Physics and Astronomy, or Materials and Nanosciences*

Course ID: 007449

**Intermediate Classical Mechanics**

Non-inertial frames of reference. Calculus of variations. Lagrangian mechanics. Coupled oscillations and normal modes. Hamiltonian dynamics. [Offered: F,S]

*Prereq: One of PHYS 236, CS 114, 116, 136, 146; One of PHYS 263 or AMATH 271; One of MATH 227, 237, 247; One of MATH 228, AMATH 250, AMATH 251*

Course ID: 007450

**Mathematical Physics 1**

Sturm-Liouville theory. Legendre, Bessel, and other special functions. Fourier series and introduction to Fourier transforms. Separation of variables. [Offered: F, S]

*Prereq: MATH 227; One of PHYS 236, CS 114, 116, 136, 146; One of MATH 228, AMATH 250, 251; Honours Physics, Chemical Physics, Physics and Astronomy, Life Physics or Materials and Nanosciences students only.*

*Antireq: AMATH 353*

Course ID: 007451

**Mathematical Physics 2**

Introduction to probability and statistics. Complex variables, Cauchy-Riemann conditions, Cauchy integral formula, Taylor and Laurent expansions, residue theorem, contour integrals and applications. Fourier and Laplace transforms with applications. [Offered: W]

*Prereq: MATH 227; One of MATH 228, AMATH 250, 251; Honours Physics, Chemical Physics, Physics and Astronomy, Life Physics and Materials and Nanosciences students only.*

*Antireq: AMATH 332*

Course ID: 007457

**Stars**

Stellar distances, masses, ages. Stellar interiors and atmospheres, star formation and evolution. Supernovae, white dwarfs, neutron stars, black holes. [Offered: W]

*Prereq: PHYS 112 or 122; One of PHYS 236, CS 114, 116, 136, 146; Two of PHYS 234, 242, 256, 275, 358, AMATH 271*

Course ID: 007458

**Molecular and Cellular Biophysics**

Cell structure and molecular composition; intermolecular interactions and hydration; protein structure and function; cytoskeletal filaments; DNA structure, packing and chromosomes; rate equations and biological dynamics (e.g., cytoskeletal polymerization); self-assembly; cell membranes; action potentials and biological electricity; molecular motors; cell motility.

*[Note: Recommended PHYS 280/BIOL 280. Offered: F,S]*

*Prereq: PHYS 112 or 122; CHEM 123 or 125*

Course ID: 013970

**Medical Physics**

Applications of physics in medicine. The course will address basic concepts of medical imaging, nuclear medicine and radiation isotopes, radiation therapy and biomedical laser applications. Nuclear structure and binding energy. Nuclear decays, radioactivity and nuclear reactions. Interaction of radiation with matter. [Offered: W]

*Prereq: PHYS 112 or 122; one of MATH 118, 119, 128, 138, 148; PHYS 280/BIOL 280*

Course ID: 007438

**Electronics**

Norton and Thévenin equivalent circuits, bipolar junction and field-effect transistors, operational amplifiers, negative feedback, noise, common circuits used for measurement and control of laboratory experiments, introduction to digital circuits. [Offered: W]

*Prereq: One of PHYS 122 (winter 2019 or later), 224, 242.*

*Coreq: PHYS 391L*

Course ID: 013645

**Physical Optics**

Fourier Optics: diffraction, dispersion, coherence, imaging. Polarization: birefringence, Jones vectors, Mueller Matrices. Fresnel Equations: optics at an interface, thin films. [Offered: W even years]

*Prereq: PHYS 256 or ECE 404; PHYS 364 or AMATH 353*

Course ID: 013659

**Biophysics of Therapeutic Methods**

The effect of radiation of various kinds on cells and tissues; elements of radiobiology and photobiology; molecular mechanisms of radiation-induced DNA damage and cell death, repair of radiation damage, dose-response relationships; tumor radiobiology and therapies, radiotherapy, photodynamic therapy, combination therapies; radiosensitizers and photosensitizers for cancer therapies; transdisciplinary advances in physical methods (ultrafast laser and ultrasound techniques) for biomedical applications.

*[Note: PHYS 380 is recommended. Offered: W even years]*

*Prereq: One of PHYS 112, 122, 125, ECE 106; One of BIOL 130, 239, CHEM 123, 125, PHARM 141, PHYS 280/BIOL 280, PHYS 380; Level at least 3A Science, Mathematics or Engineering students*

Course ID: 011381

**Biophysics of Imaging**

Introduction to imaging concepts in biophysics with emphasis on the interrelationship between the physics principles of an imaging modality and the associated image reconstruction; methods for imaging at macroscopic to microscopic scales; computed tomography, magnetic resonance imaging, ultrasound, PET, optical imaging, optical and fluorescence microscopy, scanning probe microscopy (AFM, STM), optical tweezers, electron microscopy.

*[Note: PHYS 380 recommended. Offered: W odd years]*

*Prereq: One of PHYS 112, 122, 125, ECE 106; One of MATH 128, 138, 148,(SYDE 111,112);One of PHYS 224, 233, 234, 242, 256, 280, 380, ECE 209, 370, 375, NE 232, 241, SYDE 283, AMATH 231, 373, CS 473, CHEM 209, 356; Level at least 3A SCI, MATH or ENG stdnts*

### PHYS 400s

Course ID: 007463

**Quantum Physics 3**

Symmetries and conservation laws. Review of time-independent perturbation theory (degenerate and non-degenerate, Rayleigh-Schrodinger, Brillouin-Wigner and canonical perturbation theory; effective Hamiltonian derivation). Time-dependent perturbation theory (1st and 2nd order, adiabatic perturbation, Aharonov-Bohm effect). Fermi's golden rule. Two-level systems. Emission and absorption of radiation (applications). Second quantization of electromagnetic field in free space; photons. Spontaneous emission and natural lifetime; Lamb shift. Elements of scattering theory. Introduction to the Dirac equation. [Offered: F]

*Prereq: PHYS 334 or AMATH 373; PHYS 364 or (AMATH 351 and 353)*

Course ID: 007464

**Current Topics in Condensed Matter Physics**

Physics pertaining to collective and emergent phenomena in condensed matter systems. Examples of topics to be covered include magnetism, superconductivity, heavy Fermion systems, quantum hall effect, protein folding, membranes, DNA physics, polymer physics, Modern experimental and theoretical techniques. [Offered: W]

*Prereq: PHYS 335, 359; PHYS 334 or AMATH 373*

Course ID: 007465

**Research Project**

A research project in any area of Physics approved by the course co-ordinator(s). The student is required to present a summary of the project orally and to submit a written report in a style suitable for publication. Some projects, especially those with an experimental emphasis, will likely continue as 437B. In these cases, students will submit an interim written report, in addition to the oral presentation. [Offered: F,W]

*Department Consent Required*

*Prereq: Honours Physics, Chemical Physics, Mathematical Physics, Physics and Astronomy, Materials and Nanosciences or Life Physics students only*

Course ID: 007466

**Research Project (Continued)**

A continuation of the project undertaken in PHYS 437A. The student is required to present a summary of the project orally or by poster and to submit a written report in a style suitable for publication. [Offered: W]

*Department Consent Required*

*Prereq: PHYS 437A*

Course ID: 013647

**Electricity and Magnetism 3**

Review of the origin of Maxwell's equations, conservation laws, potential formulation of Maxwell's equations and gauge choices, vacuum solutions of Maxwell's equations (free space, waveguides, dispersion), solution to Maxwell's equations for arbitrary sources (static and time-dependent problems), relativistic formulation of electrodynamics, macroscopic Maxwell's equations and plane waves in macroscopic media. [Offered: F]

*Prereq: PHYS 342; PHYS 364 or (AMATH 351 and AMATH 353)*

Course ID: 007470

**Introduction to Particle Physics**

This course introduces students to the standard model of particle physics. Topics covered include symmetries, particle classification, experimental methods and tools, scattering, Feynman diagrams, gauge theories, quantum electrodynamics, quarks, quantum chromodynamics, weak interactions, and the Higgs mechanism. [Offered: W]

*Prereq: PHYS 334 or AMATH 373; PHYS 363; (PHYS 364 and 365) or (AMATH 332, 351, 353)*

Course ID: 003369

**Quantum Theory 2**

The Hilbert space of states, observables, and time evolution. Feynman path integral and Greens functions. Approximation methods. Co-ordinate transformations, angular momentum, and spin. The relation between symmetries and conservation laws. Density matrix, Ehrenfest theorem, and decoherence. Multiparticle quantum mechanics. Bell inequality and basics of quantum computing. [Offered: F]

*Prereq: AMATH 373 or PHYS 334*

*(Cross-listed with AMATH 473)*

Course ID: 013648

**Nanophysics**

Fundamentals of nanotechnology. Applications of nanotechnology in biology and medicine. Nanotechnology and society. Physical foundations of nanodevices. Conduction at the nanoscale. Modern nanodevices. [Offered: F]

*Prereq: PHYS 335 or ECE 231; Level at least 4A.*

*Antireq: NE 471*

Course ID: 011497

**Introduction to Quantum Information Processing**

Basics of computational complexity; basics of quantum information; quantum phenomena; quantum circuits and universality; relationship between quantum and classical complexity classes; simple quantum algorithms; quantum Fourier transform; Shor factoring algorithm; Grover search algorithm; physical realization of quantum computation; error-correction and fault-tolerance; quantum key distribution. [Offered: F, W]

*Prereq: One of MATH 114, 115, 235, 245, PHYS 334; Level at least 3A*

*(Cross-listed with CS 467, CO 481)*

Course ID: 007479

**Cosmology**

Robertson-Walker metric and Friedmann equations. Observational cosmology. Dark matter and dark energy. Gravitational lensing. Big Bang nucleosynthesis, the cosmic microwave background. Inflation. Structure formation.

*[Note: PHYS 474 is recommended. Offered: F]*

*Prereq: One of AMATH 261, 271, PHYS 263; Level at least 4A in Mathematics or Science*

Course ID: 003371

**Introduction to General Relativity**

Tensor analysis. Curved space-time and the Einstein field equations. The Schwarzschild solution and applications. The Friedmann-Robertson-Walker cosmological models. [Offered: W]

*Prereq: One of AMATH 261, 271, PHYS 263; AMATH 231 or MATH 227; Level at least 4A in Mathematics or Science*

*(Cross-listed with AMATH 475)*

Course ID: 013971

**Advanced Therapeutic Concepts in Oncology and Medical Physics**

This course examines advanced oncology therapeutic concepts required as a foundation for patient management in the inpatient, ambulatory, and community settings. Topics include a comprehensive review of cancer epidemiology and pathophysiology, therapeutic agents used in the oncology setting, management of cancer therapy toxicities, and treatment and palliation of cancer symptoms. Physics methods in radiation therapy and the medical physicist's role in cancer treatment will be addressed. [Offered: W; Held with PHARM 464]

*Prereq: Level at least 4A Life Physics, Medical Physics Specialization*

Course ID: 015892

**Quantum Theory 3: Quantum Information and Foundations**

Theory of correlations and entanglement; theory of quantum channels, detectors; the measurement problem, in quantum mechanics; phase space formulation of quantum mechanics; entanglement in infinite dimensional quantum systems; introduction to open quantum systems; and exploration of current research directions in quantum information. [Offered: W]

*Prereq: AMATH 473/PHYS 454; Level at least 4A Mathematics or Science students only*

*(Cross-listed with AMATH 474)*

Course ID: 013972

**Special Topics in Life, Medical and Biophysics**

A lecture and project course offered in areas of life, medical and biophysics, which will add to the learning experience of the students in these plans at a fourth-year level. Lecture topics may include advanced topics in molecular and cellular biophysics, imaging, biophotonics, interaction of radiation with biomaterials, radiation dosimetry and other physics based diagnostics and therapeutics. Projects may include studies of recent advances in any areas of medical and biophysics.
[Offered: F]

*Prereq: Level at least 4A; one of PHYS 380, 383, 395, 396*