Concordia University

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Physics

Doctor of/Doctorate in Philosophy (Physics)

Admission Requirements. The normal requirement for admission is a Master of Science degree in Physics with high standing from a recognized university. Meritorious students enrolled in the Master of Science program in Physics at this university who have completed all requirements except for the thesis may apply for permission to proceed directly to doctoral studies without submitting a master’s thesis.

Requirements for the Degree

  1. Credits. A fully-qualified candidate, entering the doctoral program with a master’s degree, is required to complete a minimum of 90 credits.

  2. Residence. The minimum period of residence is two years (6 terms) of full-time graduate study beyond the master’s degree, or the equivalent in part-time study, or three years (9 terms) of full-time graduate study beyond the bachelor’s degree for those students who are permitted to enrol for doctoral studies without completing a master’s degree.

  3. Courses. The candidate is required to take the following:

    1. 9 credits chosen from PHYS 601, 602, 603, 609, 636, 637, 639, 642, 644, 646, 648, 649, 660, 663, 665 and 679.
      Students may, with permission of their supervisor, substitute up to two courses from the following list:
      CHEM 620 Selected Topics in Organic Chemistry
      CHEM 630 Selected Topics in Physical Chemistry
      CHEM 677 Enzyme Kinetics and Mechanism
      CHEM 678 Protein Engineering and Design
      CHEM 690 Selected Topics in Instrumentation
      CHEM 692 Experimental Protein Chemistry
      MAST 689 Variational Methods
      MAST 694 Group Theory
      MAST 840 Lie Groups
      MAST 841 Partial Differential Equations
      MAST 851 Differential Geometric Methods in Physics
      MAST 854 Quantization Methods
      MAST 855 Spectral Geometry
      MAST 856 Selected Topics in Mathematical Physics
      MAST 857 Selected Topics in Differential Geometry

    2. PHYS 861: Doctoral Seminar on Selected Topics I (3 credits), in which the candidates must present a pedagogical talk on a topic from physics to an advanced-level undergraduate student audience.

    3. PHYS 862: Doctoral Seminar on Selected Topics II (3 credits), in which the candidates must present a talk related to their thesis research to a critical audience.

    4. PHYS 870: Comprehensive Examination and Research Proposal (6 credits): The purpose of this course is to satisfy the department that the student is sufficiently prepared, in terms of background and ability, to pursue the research required for a PhD. Each student is required to prepare a written project in his/her field of research. The topic is general, and not part of the thesis work. The oral examination is based on the contents of this report. The Graduate Program Committee appoints an examination committee in consultation with the thesis supervisor. The supervisor is responsible for the subject chosen and also acts as a member of the examining committee for the oral presentation. The comprehensive examination must be completed within four months after the candidate’s initial registration in the PhD program. The grade for this course is a Pass or Fail. In case of failure in the first attempt, only one more attempt is allowed to take place.

    5. PHYS 890: Doctoral Research and Thesis (69 credits): A student who has passed the comprehensive examination is admitted to candidacy for the PhD degree. The student is allowed to continue working on a research project under the direction of a faculty member of the department only after passing the comprehensive examination. The research is in areas which reflect the interests of the faculty and the facilities of the department. The thesis must make a distinct and original contribution to knowledge, and be presented in acceptable literary form.

Academic Regulations

  1. GPA Requirement. The academic progress of students is monitored on a periodic basis. To be permitted to continue in the program, students must obtain a cumulative grade point average (GPA) of 3.00 based on a minimum of 6 credits. Students whose GPA falls below 3.00 are considered to be on academic probation during the following review period. Students whose GPA falls below 3.00 for two consecutive review periods are withdrawn from the program.

  2. C Rule. Students who obtain less than a grade of B- in a course are required to repeat the course or take another course. Students receiving more than one C grade are withdrawn from the program.

  3. F Rule. Students who receive a failing grade in the course of their PhD studies are withdrawn from the program. Students may apply for readmission. Students who receive another failing grade after readmissionare withdrawn from the program and are not  considered for readmission.

  4. Time Limit. All work for a doctoral degree must be completed before or during the calendar year, 18 terms (six years) of full-time study or 24 terms (eight years) of part-time study from the time of original registration in the program.

  5. Graduation Requirement. In order to graduate, students must have a cumulative GPA of at least 3.00.

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Master of/Magisteriate in Science (Physics)

Admission Requirements. Applicants must have an honours degree, or its equivalent in Physics. Qualified applicants lacking prerequisite courses are required to take undergraduate courses (up to 12 credits) in addition to the regular graduate program. Applicants with deficiencies in their undergraduate preparation may be required to take a one-year qualifying program before admission to the MSc program.

Requirements for the Degree

  1. Credits. A fully-qualified candidate is required to complete a minimum of 45 credits.

  2. Residence. The minimum residence requirement is one year (3 terms) of full-time study, or the equivalent in part-time study.

  3. Courses. The candidate is required to take the following:

    1. 9 credits chosen from PHYS 601, 602, 603, 609, 636, 637, 639, 642, 644, 646, 648, 649, 660, 663, 665 and 679.
      Students may, with permission of their supervisor, substitute up to two courses from the following list:
      CHEM 620 Selected Topics in Organic Chemistry
      CHEM 630 Selected Topics in Physical Chemistry
      CHEM 677 Enzyme Kinetics and Mechanism
      CHEM 678 Protein Engineering and Design
      CHEM 690 Selected Topics in Instrumentation
      CHEM 692 Experimental Protein Chemistry
      MAST 689 Variational Methods
      MAST 694 Group Theory

    2. PHYS 760: MSc Seminar on Selected Topics (3 credits). Students must give one seminar in the field of their research.


  4. PHYS 790: Master’s Research and Thesis (33 credits): The thesis must represent the results of the student’s original research work undertaken after admission to this program. Work previously published by the student may be used only as introductory or background subject matter. The thesis is examined by a departmental committee. An oral examination is conducted to test the candidate’s ability to defend the thesis.

  5. The thesis may be based on a study of a significant problem in physics or a research project conducted as part of the student’s employment. Permission to submit a thesis in the latter category is granted in the event that:
    1. the student’s employer furnishes written approval for the pursuit and reporting of the project;
    2. the student has research facilities which, in the opinion of the physics graduate studies committee, are adequate;
    3. arrangements can be made for supervision of the project by a faculty member of the Department of Physics;
    4. in all but exceptional cases, the student has direct supervision by a qualified supervisor at the site of the student’s employment. The supervisor must be approved by the physics graduate studies committee. A written working agreement between the supervisor and the university are required;
    5. the proposed topic for the thesis, together with a brief statement outlining the proposed method of treatment, is approved by the physics graduate studies committee.

Academic Regulations

  1. GPA Requirement. The academic progress of students is monitored on a periodic basis. To be permitted to continue in the program, students must obtain a cumulative grade point average (GPA) of 3.00 based on a minimum of 12 credits. Students whose GPA falls below 3.00 are considered to be on academic probation during the following review period. Students whose GPA falls below 3.00 for two consecutive review periods are withdrawn from the program.

  2. C Rule. Students in research master’s/magisteriate programs are allowed to receive no more than one C grade in order to remain in good standing in the university.

  3. F Rule. Students who receive a failing grade in the course of their studiesare withdrawn from the program. Students may apply for readmission. Students who receive another failing grade after readmission are withdrawn from the program and are not considered for readmission.

  4. Time Limit. All work for a master’s/magisteriate degree for full-time students must be completed within 12 terms (4 years) from the time of initial registration in the program at Concordia University; for part-time students the time limit is 15 terms (5 years).

  5. Graduation Requirement. In order to graduate, students must have a cumulative GPA of at least 3.00.

Courses

All courses are worth 3 credits each unless otherwise specified. The graduate courses offered by the Department of Physics fall into the following categories:

PHYS 600-609 Topics in Quantum and High Energy Physics
PHYS 630-639 Topics in Condensed Matter Physics
PHYS 640-649 Topics in Theoretical Physics
PHYS 660-669 Topics in Biomedical Physics
PHYS 670-679 Topics in Applied Physics

Topics in Quantum and High Energy Physics (600-609)

PHYS 601 Advanced Quantum Mechanics I (3 credits)
This course reviews the mathematical foundations of quantum mechanics, Heisenberg, Schroedinger, and interaction representations; time-dependent perturbation theory and the golden rule; collision theory, Born approximation, T-matrix and phase shifts; angular momentum theory: eigenvalues and eigenvectors, spherical harmonics, rotations and spin, additions theorems and their applications.
Note: Students who have received credit for PHYS 612 may not take this course for credit.

PHYS 602 Advanced Quantum Mechanics II (3 credits)
The following applications are examined: non-relativistic theory - systems of identical particles, second quantization, Hartree-Fock theory, as well as path integral formulation of quantum mechanics; relativistic theory: Dirac and Klein-Gordon equations, positron theory, propogator theory and their applications; field quantization, radiative effects, Dirac and Majorana spinors, Noether’s theorem.
Note: Students who have received credit for PHYS 613 may not take this course for credit.

PHYS 603 High Energy Physics (3 credits)
This course discusses symmetries and groups; antiparticles; electrodynamics of spinless particles, the Dirac equation and its implications for the electrodynamics of spin 1/2 particles. A general discussion of loops, renormalization and running coupling constants, hadronic structure and partons, is used to introduce the principles of Quantum Chromodynamics and Electroweak Interactions. The course concludes with an exposition of gauge symmetries, the Weinberg-Salam model, and Grand Unification.
Note: Students who have received credit for PHYS 616 may not take this course for credit.

PHYS 609 Selected Topics in Quantum or High Energy Physics (3 credits)
This course reflects the research interests of the physics faculty in quantum or high energy physics and/or those of the graduate students working with them.
Note: Students who have taken the same topic under PHYS 615, PHYS 618 or PHYS 619 may not take this course for credit.

Topics in Condensed Matter Physics (630-639)

PHYS 636 Condensed Matter Physics I (3 credits)
Review of electron levels in periodic potentials, various band-structure methods, Thomas-Fermi and Hartree-Fock theories, screening, anharmonic effects crystals, inhomogeneous semiconductors, p-n junctions, transistors. Dielectric properties of insulators, ferroelectric materials. Defects in crystals. Magnetic ordering, paramagnetism, diamagnetism, ferromagnetism, phase transitions, superconductivity.

PHYS 637 Condensed Matter Physics II (3 credits)
This course provides a review of the phonon modes and electron band structure of crystals. It covers a selection of modern quantum condensed‑matter topics which may include Hartree‑Fock, mesoscopic quantum transport theory (quantum dots, 1D systems, 2D systems), superconductivity, the quantum Hall effects, weak localization, and current research topics. Students further develop an in-depth knowledge of the course material through an individual project.

PHYS 639 Selected Topics in Condensed Matter Physics (3 credits)
This course reflects the research interests of the physics faculty in condensed matter physics and/or those of the graduate students working with them.
Note: Students who have received credit for PHYS 635 may not take this course for credit.

Topics in Theoretical Physics (640-649)

PHYS 642 Statistical Physics (3 credits)
This course covers statistical concepts, probability, Gaussian probability distribution, statistical ensemble, macrostates and microstates, thermodynamic probability, statistical thermodynamics, reversible and irreversible processes, entropy, thermodynamic laws and statistical relations, partition functions, Maxwell’s distribution, phase transformation, Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics, quantum statistics in the classical limit, black-body radiation, conduction electrons in metals, interacting particle system, lattice vibrations, virial coefficients, Weiss molecular field approximation.
Note: Students who have received credit for PHYS 654 may not take this course for credit.

PHYS 644 Advanced Classical Mechanics and Relativity (3 credits)
This course covers generalized coordinates, Lagrange’s equations, method of Lagrange multipliers, variational formulation, Hamilton’s equations of motion, canonical transformations, Hamilton-Jacobi theory, special theory of relativity, Einstein’s axioms, Lorentz transformations, form invariance and tensors, four-vectors, gravity.
Note: Students who have received credit for PHYS 658 may not take this course for credit.

PHYS 646 Electrodynamics (3 credits)
This course covers the electrostatic boundary-value problem with Green’s function, Maxwell’s equations, energy-momentum tensor, guided waves, dielectric wave-guides, fibre optics, radiation static field, multipole radiation, velocity and acceleration field, Larmor’s formula, relativistic generalization, radiating systems, linear antenna, aperture in wave guide, scattering, Thompson scattering, Bremsstrahlung, Abraham-Lorentz equation, Breit-Wigner formula, Green’s function for Helmholtz’s equation. Noether’s theorem.

PHYS 648 Non Linear Waves (3 credits)
Linear stability analysis and limitations, modulated waves and nonlinear dispersion relations, Korteweg-de Vries, sine-Gordon, and nonlinear Schrödinger equations. Hydro-dynamic, transmission-line, mechanical, lattice, and optical solitions. Applications in optical fibres, Josephson junction arrays. Inverse scattering method, conservation laws.

PHYS 649 Selected Topics in Theoretical Physics (3 credits)
This course reflects the research interests of the Physics faculty in theoretical physics and/or those of the graduate students working with them.

Topics in Biomedical Physics (660-669)

PHYS 660 Chemical Aspects of Biophysics (3 credits)
This course examines several aspects of the stability of protein structures including bonding and nonbonding interactions, energy profiles, Ramachandran plot, stabilization through protonation-deprotonation, interaction of macromolecules with solvents, the thermodynamics of protein folding, and ligand binding. The Marcus-theory of biological electron transfer is discussed. The course also introduces the students to several modern biophysical techniques such as electronic spectroscopies (absorption, fluorescence), X-ray absorption spectroscopy, NMR and EPR spectroscopy, IR and Raman spectroscopy, circular dichroism, and differential scanning calorimetry. Students further develop an in-depth knowledge of the course material through an individual project.

PHYS 663 Quantitative Human Systems Physiology (3 credits)
Prerequisite: Open to all Science and Engineering program students.
This course addresses important concepts of quantitative systems physiology and the physical bases of physiological function in different organ systems. The student becomes familiar with the structure and functional principles of the main physiological systems, and how to quantify them. These include the nervous, cardiovascular, respiratory and muscular systems. Important biophysical principles and quantitative physiological methods are presented. Topics may include the biophysics of muscle contractions, fluid dynamics in the cardiovascular system, respiration gas exchange and neuronal communication, and how the biophysics of neuronal communications can be used to image brain activity. Students develop in-depth knowledge of how to apply these principles to a specific system through an individual project.

PHYS 665 Principles of Medical Imaging (3 credits)
Prerequisite: Open to all Science and Engineering program students.
This course aims to introduce the physical principles associated with important medical imaging techniques used in medicine and in neuroscience research. The objective is to cover the whole imaging process in detail starting from the body entities to be imaged (e.g. structure, function, blood flow, neuronal activity), to the physical principles of data acquisition and finally the methods used for image data reconstruction. Important imaging modalities such as X-ray and computer tomography, magnetic resonance imaging, nuclear medicine, ultrasound, electrophysiology and optical imaging techniques are presented. Students develop an in-depth understanding of how to apply this knowledge for a specific imaging modality through an individual project.

Topics in Applied Physics (670 - 679)

PHYS 679 Selected Topics in Applied Physics (3 credits)
This course reflects the research interests of the Physics faculty in Applied Physics and/or those of the graduate students working with them.

Seminar, Thesis, and Comprehensive Examination

PHYS 760 MSc Seminar on Selected Topics (3 credits)
Students must give one seminar in the field of their research. In addition, full time students must participate in all seminars given in the department, and part time students must attend, during their studies, the same number of seminars that are normally given during the minimum residence requirement for full time students. The course in evaluated on a pass/fail basis. No substitution is permitted.

PHYS 790 Master’s Research and Thesis (30 credits)

PHYS 861 Doctoral Seminar on Selected Topics I (3 credits)
Students must present one pedagogical seminar on a topic from physics to an advanced-level undergraduate student audience. This course is evaluated on a pass/fail basis. No substitution is permitted.

PHYS 862 Doctoral Seminar on Selected Topics II (3 credits)
Students must present one seminar in their current research area to a critical audience. In addition, students are required to attend and participate in all departmental seminars. This course is evaluated on a pass/fail basis. No substitution is permitted.

PHYS 870 Comprehensive Examination and Research Proposal (6 credits)

PHYS 890 Doctoral Research and Thesis (69 credits)
Note: Students admitted prior to 1997-98 should register for PHYS 850 (70 credits). Students admitted after summer 1997 will register for PHYS 850 (66 credits).

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