# Postgraduate Courses

PHYS

Physics

- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- PHYS 5820Diffraction and Imaging Techniques in Materials Science[3-1-1:4]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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.