Study Roadmap for Physics
My Roadmap for Physics
Undergraduate Physics
- Modern Physics
- Mathematical Methods in Physics
- Classical Mechanics
- Electricity and Magnetism I, II
- Quantum Mechanics I
- Optics
- Introduction to Materials Science
- Introduction to Materials Processing
- Structure and Properties of Crystalline Solids
- Introduction to Stellar Astrophysics
- Computational Methods in Physics
- Thermodynamics and Statistical Physics
- Quantum Mechanics II
- Lasers and Optical Electronics
- Particle Physics and the Universe
- Information Physics
- Physics of Management Science
- Big Bang Cosmology and Inflation
Undergraduate Mathematics
- Multivariable Calculus
- Mathematical Analysis
- Linear Algebra
- Differential Equations
- Real Analysis
- Abstract Algebra
- Complex Analysis
- Partial Differential Equations
- Differential Geometry
Postgraduate Physics
- Mathematical Methods in Physics
- Computational Energy Materials and Electronic Structure Simulations
- Solid State Physics I
- Electro and Magneto Statics
- Electromagnetic Waves, Maxwell Equations, and Relativity
- Advanced Quantum Mechanics
- Modern AMO (Atomic Molecular Optical) Physics with Atoms and Photons
- Statistical Mechanics I
- Introduction to Quantum Many-body Theory
- Solid State Physics II
- Introduction to Quantum Field Theory
- Introduction to General Relativity
- Modern Semiconductor Physics
- Diffraction and Imaging Techniques in Materials Science
- Introduction of Topological Band Theory
- Scientific Programming and Visualization
- Many-particle Physics
- Advanced Quantum Field Theory
Details
Modern Physics
Study material
Introduction to relativity; introduction to quantum theory: particle-wave duality and Schrodinger equation; atoms, molecules; and statistical physics: Maxwell, Bose and Fermi distributions.
Mathematical Methods in Physics
Study material
- Mathematical Methods in The Physical Sciences by Mary L. Boas
Physical applications of analytic and numerical methods are studied in such topics as differential equations, Fourier series, Laplace transforms, matrices and vectors.
Classical Mechanics
Study material
- Classical Dynamics of Particles and Systems by Thornton & Marion
- Analytic Mechanics by Fowles & Cassiday
Newtonian mechanics, including rigid bodies; oscillating systems; gravitation and planetary motion; Lagrange equations; Hamilton’s equations; normal modes and small oscillations.
Electricity and Magnetism I, II
Study material
- Introduction to Electrodynamics by David j. Griffiths
A physics core course. Electrostatics: electric charge and fields, multipoles, Laplace equation, dielectrics; magnetostatics: currents, magnetic fields and vector potential, magnetic materials; Maxwell’s equations.
Electrodynamics: applications of Maxwell’s equations, propagation in various media, radiation, relativistic electrodynamics, transmission lines and wave guides.
Quantum Mechanics I
Study material
- Introduction to Quantum Mechanics by David j. Griffiths
Basic properties of Schrodinger equation, bound and scattering states in simple one-dimensional potentials, formulation of quantum mechanics in terms of Hilbert space and Dirac bracket notation, Schrodinger equation in three-dimensions, angular momentum, hydrogen atom wavefunction, systems of identical particles, spin and statistics, multi-electron atoms and the periodic table.
Optics
Study material
- Optics by Eugene Hecht
Ray tracing, matrix optics, wave optics, superposition of waves and interference, coherence, Fresnel and Fraunhofer diffraction, polarisation, Fourier optics, holography, phase and group velocity, material dispersion, propagation of Gaussian beams.
Introduction to Materials Science
Study material
- Introduction to Materials Science for Engineers by James F.Shackelford
An integrated study of the nature and behavior of metals, ceramics and polymers. Topics include crystal structures, phase diagrams, microstructures and microscopy, defects, phases and interfaces in materials systems, phase transformations, deformation, annealing and failure of materials.
Introduction to Materials Processing
Study material
- Transport Phenomena in Materials Processing by D. R. Poirier, G. H. Geiger
Phase transitions and phase diagrams, crystal growth, vacuum physics and technology, thin film preparation by physical vapor deposition, sputtering and sol-gel. Chemical processing such as chemical vapor deposition, oxidation, wet and plasma etching. Lithography and patterning techniques.
Structure and Properties of Crystalline Solids
This course covers material structures and physical properties. Topics include the periodic structure of crystals with basic crystallography, symmetry operations and crystalline structures, diffraction and microscopy techniques to determine Bravais lattices and crystal structures, the imperfections in solid materials and their roles in physical properties, physical and mechanical behavior of solid materials based on different bonding types and common defects, the fundamental concepts of mechanical, electrical, optical and magnetic properties and nanomaterials including nanotubes, nanowires, graphene, and 2D semiconductors.
Introduction to Stellar Astrophysics
Study material
- The Physics of Stars by A. C. Phillips
Stellar radiation, stellar spectrum, binary stars, interiors of stars, star formation, post-main-sequence stellar evolution, stellar remnants.
Computational Methods in Physics
Study material
- Computational Physics by Mark Newman
This course provides an introduction to basic numerical and symbolic computation. Topics include methods of interpolation and extrapolation, approximation methods of root finding, numerical integration and solving ordinary differential equations, symbolic algebra and calculus. Students need to write computer codes in laboratory sessions and write lab reports to describe their results.
Thermodynamics and Statistical Physics
Study material
- An Introduction to Thermal Physics by Daniel V. Schroeder
Laws of thermodynamics, entropy, thermodynamic relations, free energy; elementary statistical mechanics: Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics; elementary transport theory; applications to physical systems.
Quantum Mechanics II
Study material
- Principles of Quantum Mechanics by R. Shankar
This course is mainly on approximation methods in quantum mechanics. Topics include stationary state perturbation theory, variational principle, WKB method, time-dependent perturbation theory, emission and absorption of radiation, adiabatic approximation and geometric phase, scattering theory.
Lasers and Optical Electronics
Propagation of Gaussian beams, optical cavity and cavity modes, blackbody radiation and stimulated emission, laser principles and rate equations, examples of solid state, liquid, gas and semiconductor lasers, laser Q-switching and mode-locking, detection of optical radiation.
Particle Physics and the Universe
Study material
- Concepts of Elementary Particle Phyiscs by Michael E. Peskin
In this course, a systematic introduction to particle physics will be provided, with the topics mainly covering: the tool of Feynman diagrams, the Standard Model in particle physics (the zoo of fundamental particles, electroweak unified theory, and Higgs mechanism), particle physics at colliders (particularly at the Large Hadron Collider), and the interplay between particle physics and cosmology. It aims at enabling students to catch up the progress in particle physics in a timely way, and appreciate the beauty of fundamental rules in nature.
Information Physics
Probability theory, entropy in information theory, relative entropy and mutual information, Second Law of thermodynamics, instantaneous code and block code, data compression: Huffman code, portfolio management. Introduction to Mathematical Finance: Options and Binomial Tree.
Physics of Management Science
Study material
- Practical Management Science by Wayne L. Winston, S. Christian Albright
This course will introduce the concepts and techniques of optimization and modeling in the management of systems and business applications with many variables and constraints. We will discuss linear programming, network flow models, project management, nonlinear programming, queuing analysis, computer solutions, and the statistical physics of optimization in complex systems.
Big Bang Cosmology and Inflation
Study material
- Introduction to Cosmology by Barbara Ryden
In this course, a systematic introduction to modern cosmology will be provided, with the topics including: Robertson-Walker metric and Friedmann equation, spacetime evolution of the Universe, thermal history of the Universe, Big-Bang nucleosynthesis, cosmic microwave background, dark matter and dark energy, inflation. It aims at enabling students to catch up with the progress in cosmology in a timely way, and appreciate the beauty of the science on the Universe.
Undergraduate Mathematics
Multivariable Calculus
Study material
- Calculus: A Complete Course by Robert A. Adams & Christopher Essex
Sequences, series, gradients, chain rule. Extrema, Lagrange multipliers, line integrals, multiple integrals. Green’s theorem, Stoke’s theorem, divergence theorem, change of variables.
Mathematical Analysis
Study material
- Introduction to Analysis by William R. Wade
Sets and functions, real numbers, limits of sequences and series, limits of functions, continuous functions, differentiation, Riemann integration, additional topics.
Linear Algebra
Study material
- Linear Algebra Done Right by Sheldon Axler
Vector space, matrices and system of linear equations, linear mappings and matrix forms, inner product, orthogonality, eigenvalues and eigenvectors, symmetric matrix.
Differential Equations
Study material
- Elementary Differential Equations and Boundary Value Problems by William E. Boyce, Richard C. DiPrima
First and second order differential equations, initial value problems, series solutions, Laplace transform, numerical methods, boundary value problems, eigenvalues and eigenfunctions, Sturm-Liouville theory.
Real Analysis
Study material
- Principles of Mathematical Analysis by Walter Rudin
Functions of several variables, implicit and inverse function theorem, uniform convergence measure and integral on the real line.
Abstract Algebra
Study material
- A First Course in Abstract Algebra by John B. Fraleigh
Polynomials; Jordan canonical form, minimal polynomials, rational canonical form; equivalence relation; group, coset, group action; introduction to rings and fields.
Complex Analysis
Study material
- Applied Complex Variables for Scientists and Engineers by Yue Kuen Kwok
Complex differentiability; Cauchy-Riemann equations; contour integrals, Cauchy theory and consequences; power series representation; isolated singularities and Laurent series; residue theorem; conformal mappings.
Partial Differential Equations
Study material
- Partial Differential Equations by Lawrence C. Evans
Derivations of the Laplace equations, the wave equations and diffusion equation; Methods to solve equations: separation of variables, Fourier series and integrals and characteristics; maximum principles, Green’s functions.
Differential Geometry
Study material
- CALCULUS III** by Guowu Meng
- Differential Geometry of Curves and Surfaces by Manfredo P. Do Carmo
- Differential Geometry: Curves - Surfaces - Manifolds by Wolfgang Kuhnel
Curve theory; curvature and torsion, Frenet-Serret frame; surface theory: Weingarten map, first and second fundamental forms, curvatures, Gaussian map, ruled surface, minimal surface; instrinsic geometry: Theorema Egregium, Coddazi-Mainardi equations, parallel transport, geodesics, exponential map, Gauss-Bonnet theorem.
Postgraduate Physics
Mathematical Methods in Physics
Review 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.
Computational Energy Materials and Electronic Structure Simulations
This 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.
Solid State Physics I
Study material
- Condensed Matter Physics by Michael P. Marder
- Modern Condensed Matter Physics by Girvin, Yang
This 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.
Electro and Magneto Statics
Study material
- Classical Electrodynamics by John David Jackson
Coulomb 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.
Electromagnetic Waves, Maxwell Equations, and Relativity
Study material
- Classical Electrodynamics by John David Jackson
- Introduction to Fourier Optics by Joseph W. Goodman
Wave 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.
Advanced Quantum Mechanics
Study material
- Modern Quantum Mechianics by J. J. Sakurai, Jin Napolitano
Discussion 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.
Modern AMO (Atomic Molecular Optical) Physics with Atoms and Photons
Study material
- Atomic Physics by Christopher J. Foot
- ATOMIC AND OPTICAL PHYSICS I
- ATOMIC AND OPTICAL PHYSICS II
Introduction 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.
Statistical Mechanics I
Study material
- Equilibrium Statistical Physics by Michael Plischke, Birger Bergersen
Laws 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.
Introduction to Quantum Many-body Theory
Introduction 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.
Solid State Physics II
This 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
Introduction to Quantum Field Theory
Study material
- An Introduction to Quantum Field Theory by Michael E. Peskin, Daniel V. Schroeder
- Quantum Field Theory and the Standard Model by Matthew D. Schwartz
This is an introductory course on quantum field theory (QFT). The covered topics mainly include field quantization, interacting theory, quantum electrodynamics, renormalization and renormalization group.
Introduction to General Relativity
Study material
- Spacetime and Geometry: An Introduction to General Relativity by Sean M. Carrol
- A First Course in General Relativity by Bernard Schutz
This 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.
Modern Semiconductor Physics
Study material
- Physics of Semiconductors and their Heterostructures by Jasprit Singh
- Quantum Semiconductor Structures - Fundamentals and Applications by Claude Weisbuch, Borge Vinter
- Quantum Heterostructures - Microelectronics and Optoelectronics by Vladmir V. Mitin, Viatcheslav A. Kochelap, Michael A. Stroscio
- Low-dimensional semiconductor structures - fundamentals and device applications by Keith Barnham, Dimitri Vvedensky
Detailed 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.
Diffraction and Imaging Techniques in Materials Science
Fundamental 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.
Introduction of Topological Band Theory
The course will mainly cover the most recent development in the band theory, which introduces the concept of topology. Topics include Bloch theorem, energy band, Berry’s curvature, Spin Hall effect and quantum spin Hall effect, topological invariance, Chern number and Z2 index, Z2 topological insulator, topological crystalline insulator, topological semimetal and Weyl semimetal.
Scientific Programming and Visualization
This course will contain the basic skills of scientific programming in different languages, e.g. Python, Matlab and Mathematica, and various methods to visualize data in different forms. The instructor’s approval is required for taking this course.
Many-particle Physics
Green’s function method; density functional theory; interacting electron gas; linear response theory and Kubo formula; Kondo effect; superconductivity and superfluidity.
Advanced Quantum Field Theory
Effective Field Theory; Spontaneous Symmetry Breaking; Finite Temperature Field Theory; Abelian Higgs Model; Non-Abelian Gauge Theory; Quantum Chromodynamics (QCD); Non-linear Sigma Model; Electroweak Theory and the Standard Model; Nonperturbative Methods; Grand Unification.
Reference
- https://prog-crs.hkust.edu.hk/ugcourse
- https://prog-crs.hkust.edu.hk/pgcourse
- http://stellar.mit.edu/index.html
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