# Postgraduate Courses

- PHYS 5110Mathematical Methods in Physics[4-0-0:4]Previous Course Code(s)PHYS 511DescriptionReview of vector analysis; complex variable theory, Cauchy-Rieman conditions, complex Taylor and Laurent series, Cauchy integral formula and residue techniques, conformal mapping; Fourier series; Fourier and Laplace transforms; ordinary differential equations, Bessel functions; partial differential equations, wave and diffusion equations, Laplace, Helmholtz and Poisson's equations, transform techniques, Green's functions; integral equations, Fredholm equations, kernals; Rieman sheets, method of steepest descent; tensors, contravariant and covariant representations; group theory, matrix representations.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Apply Cauchy integral formula and residue techniques.
- 2.Understand calculus of variations.
- 3.Solve ordinary differential equations.
- 4.Understand common types of partial differential equations.
- 5.Apply Green function and Fourier transform in solving differential equations.
- 6.Apply conformal maps to solve differential equations.

- PHYS 5120Computational Energy Materials and Electronic Structure Simulations[3-0-0:3]Previous Course Code(s)PHYS 6810GBackgroundStudents should have basic knowledge of quantum mechanics.DescriptionThis course will introduce atomistic computational methods to model, understand, and predict the properties and behavior of real materials including solids, liquids, and nanostructures. Their applications to sustainable energy will be discussed. Specific topics include: density-functional theory (DFT), Kohn-Sham equations, local and semi-local density approximations and hybrid functionals, basis sets, pseudopotentials; Hartree-Fock method; ab initio molecular dynamics with interatomic interactions derived on the ﬂy from DFT, Car-Parrinello molecular dynamics; Monte-Carlo sampling; computational spectroscopy from ﬁrst principles, IR and Raman. Students will learn how to use free open-source packages to do materials simulations on a Linux computer cluster. Students should have basic knowledge of quantum mechanics. The instructor's approval is required for taking this course.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Explain the principles of density-functional theory, including Kohn-Sham equations, band gap discontinuity, exchange-correlation potentials, basis sets, and pseudopotentials.
- 2.Explain the Hartree-Fock (HF) method and Koopmans' theory, and describe the basic principles of post-HF methods: Cl, MP2, and CCSD.
- 3.Explain the principles of molecular dynamics and identify the relation between classical and quantum molecular dynamics.
- 4.Assess the electronic and vibrational properties of molecules or nanostructures using an open-source DFT code.
- 5.Assess the band structures and transport properties of crystal materials using an open-source DFT code.

- PHYS 5170Solid State Physics I[3-0-0:3]Previous Course Code(s)PHYS 6810ABackgroundStudents should have good understanding in undergraduate level quantum mechanics before taking this course.DescriptionThis is an introductory course on postgraduate level solid state physics. The topics covered include: electronic band structures of solids, phonons, electron dynamics in crystals, electron interactions in solids, linear response theory, electronic transitions and optical properties of solids, electron phonon interactions, integer quantum Hall effects, superconductivity and magnetism.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Derive the electronic band structures of materials with simple lattices.
- 2.Calculate phonon band structures.
- 3.Calculate the energy of electronic systems using Hatree-Fock approximations.
- 4.Formulate the electron responses to external electric and magnetic fields.
- 5.Derive the expression of the conductance of Quantum Hall Systems.
- 6.Calculate physical properties of superconductors and magnets.

- PHYS 5200Electro and Magneto Statics[4-0-0:4]Previous Course Code(s)PHYS 520DescriptionCoulomb and Gauss's law, Poisson and Laplace Equations, Green's functions, methods of images, solution of boundary value problems, special functions expansions, electrostatics of dielectrics, local fields, magnetostatics, conservation laws and Maxwell equations.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Understand the concept of electric field flux conservation and Gauss Law.
- 2.Apply Gauss law to solve practical electrostatic problems.
- 3.Understand Green theorem and the uniqueness theorem.
- 4.Apply uniqueness theorem in constructive solutions to boundary value problems.
- 5.Apply basis function expansions to solve boundary value problems.
- 6.Understand Faraday’s law and the Maxwell equations.

- PHYS 5210Electromagnetic Waves, Maxwell Equations, and Relativity[4-0-0:4]Previous Course Code(s)PHYS 521DescriptionWave solutions of the Maxwell equations, electromagnetic wave propagation, scattering, and diffraction; Fourier optics; dielectric constant of metals and dielectrics and its analytic properties; guided waves; radiation by accelerating charges; special relativity and the transformation of Maxwell equations; radiation by moving charges.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Undertand the general no-source solution form of the Maxwell equations.
- 2.Apply transmission matrix approach to solve multi-layer problems.
- 3.Undersand Kramers-Kronig relation and time-domain behavior of the response function.
- 4.Understand dipole radiation, scattering, and apply on the related phenomena—blue sky, critical opalescence.
- 5.Understand relativity.
- 6.Understand Lienart-Wiechert potential and radiation of point charges.

- PHYS 5260Advanced Quantum Mechanics[4-0-0:4]Previous Course Code(s)PHYS 526DescriptionDiscussion of various applications of quantum mechanics, such as collision theory, theory of spectra of atoms and molecules, theory of solids, second quantization, emission of radiation, relativistic quantum mechanics.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Explain why one needs to use a set of vectors to describe the state of a system rather than real numbers.
- 2.Use the Schrodinger equation to solve some simple problems.
- 3.Apply the concepts and principles to understand some phenomena in atomic and condensed matter physics.
- 4.Understand of angular momentum and its properties.
- 5.Understand of relationships between symmetries, conservations, and degeneracy.
- 6.Understand and apply the formulations of perturbation theories and traditional approximation methods.

- PHYS 5280Modern AMO (Atomic Molecular Optical) Physics with Atoms and Photons[3-0-0:3]Previous Course Code(s)PHYS 6810FDescriptionIntroduction to modern atomic physics with ultracold atoms and photons. The basic theoretical tools for atom optics and quantum optics will be introduced. Recent research works will also be covered including many-body states in optical lattices and synthetic topological states in ultracold atoms.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Explain how to describe the quantum state of atoms and photons.
- 2.Exemplify various quantum control methods.
- 3.Analyze how to manipulate atoms and molecules.
- 4.Analyze the quantum information processing.
- 5.Describe how useful quantum states can be prepared.
- 6.Apply the fundamentals to understand the modern research topics in quantum science.

- PHYS 5310Statistical Mechanics I[3-0-0:3]Previous Course Code(s)PHYS 531DescriptionLaws and applications of thermodynamics, kinetic theory, transport phenomena, classical statistical mechanics, canonical and grand canonical ensemble, quantum statistical mechanics, Fermi and Bose systems, non-equilibrium statistical mechanics.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Explain how the core principles of thermodynamics can be derived from the statistical mechanics of N-particle systems.
- 2.Use the basic tools of statistical mechanics (such as the partition function) to predict the macroscopic properties of a system from a given microscopic model.
- 3.Apply these tools in conjunction with appropriate approximation techniques to solve problems in a variety of physical systems, including (but not limited to) fluids and interacting assemblies of spins in magnetic fields.
- 4.Use the tools of statistical physics to predict the behaviour of systems in the neighbourhood of a phase transition..

- PHYS 5340Introduction to Quantum Many-body Theory[4-0-0:4]DescriptionIntroduction to theoretical methods for quantum many-body systems. Perturbative methods, like Green's functions and diagrammatics, will be introduced. Topics in response theory and quantum magnetism will be covered. More modern, entanglement-based approaches, like tensor networks, will also be discussed.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Describe the basic principles for perturbative treatment of a quantum many-body system.
- 2.Compute physical properties of certain paradigmatic quantum systems.
- 3.Discuss how simplified models of real materials arise.
- 4.Identify possible approximate methods for treating an interacting system.
- 5.Connect the notion of quantum entanglement with quantum phases of matter.
- 6.Apprehend, assimilate, and articulate latest research developments in quantum science.

- PHYS 5370Solid State Physics II[3-0-0:3]Previous Course Code(s)PHYS 6810BBackgroundStudents should have good understanding in undergraduate level quantum mechanics and undergraduate level solid state physics before taking this course.DescriptionThis is a second course on postgraduate level solid state physics. The thermal, electronic, magnetic and optical properties of solid will be studied. Semiconductor devices and electronics will be discussed. The theory of conventional and unconventional superconductors will be introduced. Special topics related to current research in solid state physics will be covered. These special topics include graphene, topological insulators, transition metal dichalcogenides and topological superconductors.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Derive the electronic band structures of graphene and transition metal dichalcogenides.
- 2.Calculate the energy spectrum of topological insulators.
- 3.Calculate the single particle excitation spectrum of topological superconductors.
- 4.Formulate the relation between electric and thermal currents in metals.
- 5.Calculate the optical and magnetic responses of solids.
- 6.Formulate the phenomenological and microscopic theories of superconductivity.

- PHYS 5410Numerical Modeling in Physics[3-0-2:3]Exclusion(s)MSDM 5004BackgroundUG level physics, working knowledge of the programming language C or C++DescriptionThis course provides students with training in performing numerical simulations in physics problems. Topics include linear algebra, ordinary and partial differential equations, and stochastic processes. Numerical techniques learned in these areas will be used to solve various problems in classical, atomic, condensed matter, statistical, and bio-physics.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Apply the numerical methods for derivatives and integrals and understand their errors.
- 2.Apply the numerical methods for interpolation, extrapolation, and least squares fitting.
- 3.Apply numerical methods to solve linear algebraic equations.
- 4.Apply numerical methods to solve ordinary differential equations and partial differential equations.
- 5.Apply mathematical optimization.
- 6.Apply Monte Carlo simulations.

- PHYS 5520Introduction to Quantum Field Theory[4-0-0:4]Previous Course Code(s)PHYS 6810DExclusion(s)PHYS 6810KBackgroundUndergraduate level classical mechanics, electrodynamics and quantum mechanics.DescriptionThis is an introductory course on quantum field theory (QFT). The covered topics mainly include field quantization, interacting theory, quantum electrodynamics, renormalization and renormalization group.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Recognize the connection between nonrelativistic quantum mechanics and quantum field theory.
- 2.Pursue quantization for scalar, spinor and vector fields.
- 3.Calculate particle scattering cross section and its decay width using Feynman rules.
- 4.Calculate quantum processes in electrodynamics at both tree and loop levels.
- 5.Pursue parameter renormalization for a given field theory.
- 6.Analyze the evolution of coupling constants and mass parameters in a given field theory.

- PHYS 5530Introduction to General Relativity[4-0-0:4]Previous Course Code(s)PHYS 6810EBackgroundUndergraduate-level classical mechanics, electrodynamics and mathematicsDescriptionThis is an introductory course on general relativity (GR). The covered topics mainly include Einstein field equation and its application in black hole physics, gravitational waves astronomy and Friedman cosmology.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Pursue the General Relativity (GR) calculations using the tool of differential geometry.
- 2.2. Use GR to study black hole physics.
- 3.Use GR to calculate gravitational radiation.
- 4.Use GR to analyze the evolution of the universe.

- PHYS 5810Modern Semiconductor Physics[3-0-0:3]Previous Course Code(s)PHYS 581Co-list withNANO 5200Exclusion(s)NANO 5200BackgroundPHYS 4052 or equivalentDescriptionDetailed explanations of the electronic, vibrational, transport, and optical properties of semiconductors based on quantum mechanics. Emphasis on nanostructured heterostructures, quantum size and low-dimensional effects, and application to modern electronics and opto-electronics.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Apply the fundamental knowledge from Quantum Mechanics and Solid State Physics to explain new physical phenomena and new or improved device operations that low dimensional semiconductor heterostructures can offer.
- 2.Explain the basic principles of common experimental methods for structural, electrical and optical characterizations of low dimensional semiconductor heterostructures.
- 3.Demonstrate the team work, independent learning, and scientific presentation skills.

- PHYS 5820Diffraction and Imaging Techniques in Materials Science[3-1-0:3]Previous Course Code(s)PHYS 582Co-list withNANO 5250Exclusion(s)NANO 5250DescriptionFundamental crystallography; crystalline structure and defects; X-ray and electron diffractions; imaging contrast mechanisms; structure determination; analytical electron microscopy. The instructor's approval is required for taking this course.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Apply the fundamental knowledge from crystallography and physics to explain the phenomena of high energy electron beams in diffraction and imaging of solid materials.
- 2.Explain the basic principles of experimental methods for determining atomic structures, interactions between electrons and solid crystalline materials and application in nanomaterials and nanotechnology.
- 3.Demonstrate the independent learning, scientific presentation skills and ability to solve materials science problems.

- PHYS 6000Physics Seminar[0-1-0:1]Previous Course Code(s)PHYS 600DescriptionSeminar topics presented by students, faculty and guest speakers. The seminars can be in the form of mini-workshops or activities organized by the Department. Graded PP, P or F.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Acquire a comprehensive set of discipline-specific professional skills and knowledge for their personal growth and career development.

- PHYS 6100Individual Study in Physics[1 credit]Previous Course Code(s)PHYS 610DescriptionThis course covers in-depth study on topics selected by the instructor on the basis of individual postgraduate student's request. The instructor's approval is required for taking this course.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Conduct literature review.
- 2.Write professional researh paper or report.
- 3.Obtain in-depth understanding on a specific research topic in related to physics.
- 4.Explain working principles or apply experimental techniques on a research topic related to physics.

- PHYS 6770Professional Development in Science (Physics)[0-2-0:2]DescriptionThis two-credit course aims at providing research postgraduate students basic training in ethics, teaching skills, research management, career development, and related professional skills. This course lasts for one year, and is composed of two parts, each consisting of a number of mini-workshops. Part 1 of the course is coordinated by the School; and Part 2 consists of some department-specific workshops which are coordinated by the department. Graded PP, P or F.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Become an effective teaching assistant (TA) by completing the TA training course.
- 2.Work safely in the research lab after completed the Safety Orientation and Laboratory Safety Training course.
- 3.Improve skills on research management, communication and manuscript preparation.
- 4.Good knowledge in some latest and leading physics research works beyond his/her area of specialization.
- 5.Have a high standard on research integrity and ethnics.

- PHYS 6771Professional Development in Physics[0-1-0:1]Exclusion(s)PHYS 6000, PHYS 6770DescriptionThis one-credit course aims at providing physics research postgraduate students discipline-specific trainings such as ethics, teaching skills, research management, career development, entrepreneurship and other professional skills. Graded PP, P or F.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Demonstrate the basic skills for research management.
- 2.Apply basic knowledge for teaching.
- 3.Demonstrate the basic skills for planning career development.
- 4.Apply knowledge in entrepreneurship and innovation.

- PHYS 6810Special Topics[1-4 credit(s)]Previous Course Code(s)PHYS 681DescriptionOfferings are announced each term. Typical topics are group theory, superfluids, stellar evolution, plasma physics, low-temperature physics, X-ray spectroscopy and diffraction, nuclear magnetic resonance, non-linear dynamics, collider physics.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Explain working principles and fundamental concepts of an advanced topic in offering.
- 2.Apply the working principles to solve typical phsyics problems in the special topic.
- 3.Obtain knowledge beyond normal courses in offering, typically in a more advanced research topic or about a technique.

- PHYS 6820Special Topics II[1-4 credit(s)]Previous Course Code(s)PHYS 682DescriptionOfferings are announced each term. Typical topics include wave scattering and mesoscopic phenomenon. Graded P or F.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Explain working principles and fundamental concepts of an advanced topic in offering.
- 2.Apply the working principles to solve typical phsyics problems in the special topic.
- 3.Obtain knowledge beyond normal courses in offering, typically in a more advanced research topic or about a technique.

- PHYS 6990MPhil Thesis ResearchPrevious Course Code(s)PHYS 699DescriptionMaster's thesis research supervised by a faculty member. A successful defense of the thesis leads to the grade Pass. No course credit is assigned.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Demonstrate research contriutions in form of a thesis.
- 2.Demonstrate research achievements, on knowledge in advanceing a research field related to physics, in the form of thesis.
- 3.Defend the research achievements and contributions through seminar or oral examination.

- PHYS 7990Doctoral Thesis ResearchPrevious Course Code(s)PHYS 799DescriptionOriginal and independent doctoral thesis research. A successful defense of the thesis leads to the grade Pass. No course credit is assigned.Intended Learning Outcomes
On successful completion of the course, students will be able to:

- 1.Demonstrate research contriutions in form of a thesis.
- 2.Demonstrate original research achievements with impact on a research field related to physics, in the form of thesis.
- 3.Defend the research achievements and contributions through seminar or oral examination.