Prerequisite & Preclusion(s): please refer to NUSMODS

Level |
Code |
Module |
Semester 1 |
Semester 2 |
Special Term |

GEMs | COS2000 | Computational thinking | Lai Choy Heng, Ng Siow Yee | Lai Choy Heng, Ng Siow Yee | |

GEH1018 | A Brief History of Science | Thomas Osipowicz | |||

GEH1027 | Einstein's Universe & Quantum Weirdness | Phil Chan | |||

GEH1028 | The Emerging Nanoworld | Andrivo Rusydi | |||

GEH1030 | Science of Music | Bernard Tan | |||

GEH1032 | Modern Technologies in Health & Medical Care | Chan Taw Kuei | Chan Taw Kuei | ||

GEH1033 | How the Ocean Works | Chammika Udalagama | |||

GEH1034 | Clean Energy and Storage | Nidhi Sharma | |||

GEH1035 | Physical Questions in Everyday Life | Ng Wei Khim | Ng Wei Khim | ||

GEQ 1000 | Asking questions | Phil Chan | Phil Chan | ||

GET1013 | Physics in the Life Sciences | Duane Loh | |||

GET1014 | The Art of Science, the Science of Art | van der Maarel, Johan | |||

GET1024 | Radiation – Scientific Understanding and Public Perception | Chung Keng Yeow | |||

GET1042 | Sky and Telescopes | Abel Yang | Abel Yang | ||

GET1043 | Universe, Big Bang, and Unsolved Mysteries | Cindy Ng | |||

GEH1031 | Understanding the Universe | Cindy Ng |

Brief Description of Modules

This module introduces students to computational thinking as applied to problems in science. A selection of examples will be chosen to illustrate (a) application of abstraction, decomposition and pattern recognition in problem formulation and solution development, and (b) solution interpretation, as well as (c) analysis of the computational solutions and data visualization. The selection will tackle different types of approaches typically used in scientific computational thinking, including deterministic, probabilistic and approximation methods. The module will also highlight scientific computational issues such as accuracy and convergence of numerical results. Python/Python Notebook (Jupyter) will be used as the computation platform.

**GEH1018 A Brief History of Science**

Nowadays it is all too easy to take basic science laws and theories, such as Newton's law of gravitational attraction or evolution for granted. The impact of research breakthroughs on society at the time of their development is being forgotten, as they come to be taken for granted. Even Science students tend to be unaware of how modern concepts have arisen, what their impact was at the time and how they changed the world. This course is intended to explain the history and significance of scientific developments on societies and how perceptions of the world have changed as a result.

**GEH1027 Einstein's Universe and Quantum Weirdness**

Einstein's Ideas of our Universe and his Quantum contributions has greatly impacted the human societies. Students will also be enthused with the historical and philosophical development of Relativity and Quantum Theories. Einstein's relativistic thinking eventually leads to the creation of navigational systems that are used in transportation and communication, both by the military as well as hand phone consumers. The construction of nuclear plants is made possible by the relativistic results of mass and energy conversion. Einstein's Photoelectric discoveries also pave the way for modern cameras in the ubiquitous mobile devices. The quest for new quantum particles at the colliders by huge collaborations among many countries gave birth to the World Wide Web and the internet Culture.

**GEH1028 The Emerging Nanoworld**

This module will acquaint students with the rapid development of the nanoworld with insights into the impact of this emerging technology on our society, environment and human life. The essence of nanoscience and technology lies in the understanding and manipulation of molecules. The advances in these fields are expected to significantly influence our lives in the spheres of medical, engineering, ethical and environmental issues. This module will discuss the potential benefits and challenges of novel nanotechnologies. How does nanotechnology affect society and human interaction? How will nanodevices and nanomaterials change our lives in the future?

**GEH1030 Science of Music**

This module aims to establish clear relationships between the basic elements of music found in virtually all musical cultures and their underlying scientific and mathematical principles. Musical scales which are the foundation of western musical culture as well as many other musical cultures will be discussed, with their evolution viewed from both western and non-western perspectives. The scientific and technical basis for the development of musical instruments of different musical cultures such as the piano, as well as their acoustical characteristics, will be examined. The module also looks at contemporary technologies in music such as digitization which has profoundly affected how the music of virtually all musical cultures is propagated.

**GEH1032 Modern Technologies in Health & Medical Care**

The human race has entered an epoch where life span has increased significantly. During the twentieth century, life span has increased from around 50 to over 75 years mainly due to antibiotics, vaccinations, and improved nutrition. However this increase in lifespan has brought to the forefront a rise in many age-related diseases. These diseases, which include cancer, heart disease, Alzheimer?s disease, Parkinson?s disease, are now a focus of health care in the 21st century. This course describes many of these diseases, and their diagnosis and treatment using advanced technology found in modern hospitals. The course also provides an insight into the scientific principles underlying these new and powerful technologies.

**GEH1033 How the Ocean Works **

About three-quarters of the surface of our home, the Earth, is covered by an ocean of water! The ocean is inseparably intertwined with human settlements. Day in, day out, directly, indirectly - from the air that we breathe to climate change, trade, politics or social holidays - the presence and the influence of the ocean is undeniable on the human society. We will discuss how the ocean is connected to our lives, how the various ocean phenomena affect our lives and our attempts at controlling and exploiting the ocean. Students will gain an appreciation of the scientific principles involved. This course will also help us make educated decisions about our environment and our ocean, so that future generations may also enjoy the majesty of our blue planet, as we do now.

**GEH1034 Clean Energy and Storage**

Modern civilization, which on the one hand boasts of having discovered the behaviour of subatomic particles, has also to its credit the impending intensified energy crisis and global warming. The urgent need to address these challenges has now become obvious. The course will acquaint students with the role of scientific development towards understanding the current global energy crisis and global warming. Emphasis will be given on how scientific progress has helped us in understanding the principle and development of various clean energy and storage technologies, their potential and applicability in present day scenarios and in shaping future energy systems.

**GEH1035 Physical Questions from Everyday Life **

This module demonstrates the application of physical science to everyday situations besides to excite the curiosity and imagination of the students and bring out their awareness of the many marvels that surround them. Students will develope a deeper knowledge and a greater appreciation towards apparently mundane events of their daily life. Everyday phenomenon relate to physical concepts will be discussed in the context to real-world topics, societal issues, and modern technology, underscoring the relevance of science and how it relates to our day-to-day lives. During the module, students will select and discuss their own apparently mundane event and present their topic accordingly.

**GEQ1000 Asking Questions**

There are many ways to ask questions, and many kinds of questions that different disciplines investigate. For a start, this module introduces six dominant modes of questioning from the perspective of computational thinking, design thinking, engineering, philosophy, science, and social sciences. These six perspectives serve as a starting point to introduce all undergraduate students to different modes of questioning across these disciplines, and provide an initial exposure to how scholars from these disciplines pursue specific lines of questioning of everyday issues. We emphasize that while there is only limited time and space within one module to devote to specific disciplinary lines of investigations, we encourage all students to actively think about other lines of questioning, other questions that need to be asked, particularly in disciplines not represented in this introductory platform as we move through this journey together. We expect that in future subsequent offerings, other disciplinary modes of investigations may also be introduced.

**GET1014 The Art of Science, The Science of Art **

It often seems the worlds of science and art are unrelated: Logical truth versus emotional imagination. Still, science and art have much in common. Science has caused paradigm shifts in artistic expression while art is used for engineering design and communication of scientific knowledge. In this module, students will be introduced to the use of materials and technology related to architecture, sculpture, painting, photography and imaging. The use of technology for dating and attribution of objects of art as well as the use of visual art for scientific illustration and design will be examined. Knowledge of the scientific principles of various forms of visual art will also be explored. The module aims at the development of some artistic skills for illustrations of scientific concepts and engineering designs. This module will help students to better express their thoughts through artistic expression and appreciate visual art.

**GET1013 Physics in Life Sciences**

Life science is the science that deals with phenomena regarding living organisms. It includes branches such as biology, medicine, anthropology and ecology. Physics on the other hand, studies the fundamental relationship between matter, energy, space, and time. Many people may consider them to be in different regimes and require different mindsets to work on. But as both disciplines advanced, it became increasingly clear that the interactions between them are far more pervasive and fundamental than one might expect. For example, the field of biophysics has risen since the 1950s, and it has vastly changed how biologists look at living systems or study biology. It proved that the mindsets of biology and physics can join together to provide deeper insight into the phenomenon we call life. We will base the material on the basic laws of physics, and discuss how they are interwined with all kinds of life science and daily life phenomena, from cells to ecosystems and from Earth to outer space. Through reading this module, the students would be able to think deeper about the daily phenomena around them, and understand better the foundation of life on Earth.

**GET1024 Radiation - Scientific Understanding and Public Perception**

This module aims to equip students with the essential knowledge to make intelligent assessments on the potential risks and uses of radiation in our modern society. After introducing the physics behind various forms of radiation, we will look at how these radiations are used in medical diagnosis and treatment and other applications. Some controversial issues in these applications will be raised and debated. The health effects of high and low levels of radiation will be presented based on scientific evidence thus dispelling some of the negative misconceptions of radiation and irrational fear of it. The social and political dynamics in electricity generation through nuclear power plants in various countries will also be discussed.

**GET1042 Sky and Telescopes**

The objective of this module is to provide a practical introduction to the skies and optical equipment. Students will learn the movements of celestial objects, their properties and telescopic instrumentations. In addition, there will be astronomy field trips, observatory visits and students will learn how to read star charts, operate telescopes and take astro-photographs.

**GET1043 Unverse, Big Bang and Unsolved Mysteries**

In this module, students will explore the universe, its contents, properties, evolution, and origin. Major topics to be covered include ideas and concepts of the universe, astronomical observations, scientific models, big bang theory, and unsolved problems in cosmology.

**GEK1520/PC1322 Understanding the Universe**

The first part of the module covers the observations of celestial objects and their influences on the ancient cultures. Students will learn how calendars and astrology were developed, and how the fundamental laws of nature were discovered. The second part covers the use of telescopes and space missions to explore the universe. Discoveries of stars and galaxies and their impact on mankind's perceptions of the Universe will be explored. Students will learn how Earth formed as a planet that develops and sustains life. There will be a discussion on the latest developments in searching for Earth-like extraterrestrial objects, and explore their impacts on the societies.

Level |
Code |
Module |
Semester 1 |
Semester 2 |
Special Term |

1000 | PC1141 | Physics I: Introduction to Classical Mechanics | Wang Qinghai | ||

PC1142 | Physics II: Introduction to Thermodynamics & Optics | Peter Ho | |||

PC1143 | Physics III: Introduction to Electricity & Magnetism | Kenneth Hong | |||

PC1144 | Physics IV: Introduction to Modern Physics | Dzmitry Matsukevich | |||

PC1221 | Fundamentals of Physics I | Tay Seng Chuan | Sharon Lim | ||

PC1222 | Fundamentals of Physics II | Dzmitry Matsukevich | Lydia Lam | ||

PC1421 | Physics for Life Sciences | Wang Zhisong | |||

PC1431 | Physics IE | Yeo Ye, Raditya Weda Bomantara | Nidhi Sharma | ||

PC1432 | Physics IIE | Nidhi Sharma | Paul Lim, Tan Meng Chwan, Quek Su Ying | ||

PC1433 | Mechanics and Waves (ESP) | Zhang Chun | |||

Labs Engineering | Wang Qinghai (coord) | Wang Qinghai (coord) | |||

Labs Physics | Ng Siow Yee (coord) | Ng Siow Yee (coord) | |||

SP1201P | Freshmen Seminars | Nidhi Sharma, Liu Xiang Yang | Andrivo Rusydi, Christian Miniatura |

Brief Description of Modules

**PC1141 Introduction to Classical Mechanics**

This module presents the fundamental principles of classical mechanics. It covers such topics as kinematics, Galilean transformation, Newton's laws of motion, dynamics of a particle with generalization to many particle systems, conservation laws, collisions, angular momentum and torque, motion of a rigid body, gravitation and planetary motion, static equilibrium, oscillatory motion and vibrational modes, waves, Doppler's effect and fluid mechanics. The module also has a practical component consisting of five experiments designed to enhance students' understanding of some of the concepts discussed in lectures. This module is targeted at science students who wish to acquire a working knowledge of mechanics, and is an essential for physics majors.

**PC1142 Introduction to Thermodynamics and Optics**

This module covers the fundamentals of two branches of physics: thermodynamics and optics. Its aim is to prepare students for a host of more advanced modules in these and related areas. Topics included in the part on thermodynamics are thermal processes and effects, the first and second laws, kinetic theory of gases, heat engines and entropy. The part on optics encompasses topics such as geometric optics, systems of lenses, optical instruments, interference, diffraction, grating and polarization. The module also has a practical component consisting of five experiments designed to enhance students' understanding of some of the concepts discussed in lectures. This module is targeted at science students who wish to acquire a working knowledge of thermodynamics and optics, and is an essential for physics majors.

**PC1143 Introduction to Electricity & Magnetism**

This module covers the fundamentals of electricity and magnetism: electric fields, electric flux and Gauss's law, electric potential; capacitance, dielectrics, current and resistance; DC circuits; magnetic fields, magnetic effect of currents, Ampere's law, electromagnetic induction; AC circuits; magnetism in matter; electromagnetic waves. The module also has a practical component consisting of five experiments designed to enhance students' understanding of some of the concepts discussed in lectures. This module is targeted at science students who wish to acquire a working knowledge in electricity and magnetism, and is an essential for physics majors.

**PC1144 Introduction to Modern Physics**

This module introduces the ideas of modern physics to students, with an emphasis on conceptual understanding. Topics covered are a) Einstein's theory of special relativity, including time dilation, length contraction, and his famous equation E=mc2, b) Quantum physics, where the observed phenomena of black body radiation, the photoelectric effect and Compton scattering, leading to the quantization of angular momentum and energy, atomic transitions and atomic spectra, c) Introduction to quantum mechanics, introducing the Heisenberg uncertainty principle, wave-mechanics and wave particle duality, and the use of wavefunctions in predicting the behaviour of particles trapped in potential wells, d) Nuclear physics, introducing radioactivity and decay processes, nuclear interaction and binding energy, fission and fusion, and e) Sub-atomic elementary particles and their classification. The module is targeted at science students who are interested in learning about the more recent developments in physics, and is an essential for physics majors.

**PC1221 Fundamentals of Physics I**

This module aims to bridge the gap between O level physics and 1st year university physics level. The syllabus covers: vectors, linear motion, velocity, acceleration, equations of kinematics, linear momentum, conservation of energy and linear momentum, forces, laws of motion and applications, work, energy, power, conservation laws, gravitation, circular motion, temperature, zeroth law, first law of thermodynamics, heat, heat capacity, ideal gas laws, thermal expansion of solids and liquids, work and heat transfer in thermodynamic processes.

**PC1222 Fundamentals of Physics II**

This module aims to bridge the gap between O level physics and 1st year university physics level. The module strives to comprehend and appreciate Nature through study of basic electromagnetic and optics phenomena. Major topics are: Coulomb's law, electric field and potential, capacitance, electric current, Ohm's law, magnetic field and flux, refraction, Snell's law, thin lenses, interference and diffraction of light waves, energy-mass relation, photo-electricity, and radioactivity.

**PC1421 Physics for Life Sciences**

This module provides a comprehensive and basic physics training within a single semester for first-year students from life sciences. It will cover mechanics, thermodynamics, electromagnetism, optics plus a few topics in atomic and nuclear physics. The specific contents have been chosen according to their relevance to life sciences as well as their importance in the conceptual framework of general physics.

**PC1431 Physics IE**

The module is designed to provide a clear and logical introduction to the concepts and principles of mechanics and thermodynamics, with illustrations based on applications to the real world. Topics covered include motion in one dimension; curvilinear motion; circular motion; relative motion; Newton's laws; friction; work and energy; conservative forces, conservation of energy; linear momentum and conservation, collisions; rotational kinematics; moment of inertia and torque; rotational dynamics; conservation of angular momentum; gravitational force, field and potential energy; planetary motion; temperature and the zeroth law, temperature scales; thermal expansion of solids and liquids; heat and internal energy, specific heat capacities, enthalpy and latent heat, work for ideal gases, first law of thermodynamics; equipartition of energy, mean free path; entropy and the second law, heat engines; entropy changes for reversible and irreversible processes. The module is targeted essentially at Engineering students.

**PC1432 Physics IIE**

This module introduces fundamental concepts of physics and is illustrated with many practical examples. Topics covered include a) Electricity and magnetism, where the basic concepts of electric and magnetic fields, forces on charged particles, electric potential, electromotive force, work and energy, are described. The properties of basic electrical circuits comprising resistors, inductors and capacitors are discussed, along with analysis of their transient and steady-state behaviour. Understanding the role of Maxwell's equations in electromagnetism is emphasized; b) Waves, introducing properties of waves, including geometric optics, propagation, interference and diffraction, and electromagnetic waves; and c) Quantum physics, where new physics concepts which led to the quantization of energy are introduced, leading to an explanation of atomic transitions, atomic spectra and the physical and the chemical properties of the atom. The uncertainty principle, wave-mechanics and wave particle duality concepts are covered, together with the use of wavefunctions in predicting the behaviour of trapped particles. The module is targeted essentially at Engineering students.

**PC1433 Mechanics and Waves**

The module consists of two parts. In Part 1, students will be introduced to the concepts and principles of mechanics of rigid bodies and their applications to solve practical problems. The topics to be covered include: force systems, equilibrium, kinematics of particles, kinetic of particles, work and energy, impulse and momentum, kinetics of system of particles, kinematics of rigid bodies, damped and undamped vibrations. In Part 2, students will be introduced to the fundamentals of wave mechanics. General description of wave propagation; types of waves: longitudinal, transverse and circular waves; speed of a travelling wave; propagation of energy and momentum; power and intensity; sound waves, oscillations of a string; light waves; superposition of waves; interference; standing waves, resonant waves; harmonics; resonance.

Level |
Code |
Module |
Semester 1 |
Semester 2 |
Special Term |

2000 | PC2020 | Electromagnetics for Electrical Engineers | Sow Chorng Haur, Yeo Ye, Ng Wei Khim | Sow CH, Yeo Ye | |

PC2130 | Quantum Mechanics I | Valerio Scarani | |||

PC2130B | Applied Quantum Physics (ESP) | Shen Lei (ESP) | |||

PC2131 | Electricity and Magnetism I | Jose Carlos Viana Gomes | |||

PC2132 | Classical Mechanics | Yeo Ye | |||

PC2133 | Applied Solid State Physics (ESP) | Jeroen Van Kan & Ho Ghim Wei (ESP) | |||

PC2134 | Mathematical Methods in Physics I | Kenneth Hong | Kenneth Hong | ||

PC2193 | Experimental Physics I | Wang Xuesen (coord) | Wang Xuesen (coord) | ||

PC2230 | Thermodynamics and Statistical Mechanics | Loh Huanqian | |||

PC2267 | Biophysics I | Garaj Slaven & Mirsaidov Utkur | |||

Labs biophysics | Vd Maarel (coord), Wang Z, Garaj, Mirsaidov | Vd Maarel (coord), Wang Z, Garaj, Mirsaidov | |||

SP2251 | Science at the Nanoscale | A Wee & Chin W S (Chem) |

Brief Description of Modules

**PC2020 Electromagnetics for Electrical Engineers**

This module is an introduction to electromagnetics (EM) for electrical engineers. Electromagnetics is essential in all disciplines of electrical engineering. At the end of this module, students will be able to explain many physical phenomena in everyday life, such as electricity energy transmission, wave reflection/transmission, and the impact of skin depth on wave propagation. Topics covered include: static electric fields, static magnetic fields, timevarying fields, electromagnetic waves, transmission lines and antennas.

**PC2130 Quantum Mechanics I**

This module provides a rigorous introduction to quantum mechanics. It covers the following list of topics: Description of quantum systems: Hilbert space; observables, eigenfunctions, the statistical interpretation, the uncertainty relations; pure and mixed states using density matrices and the Dirac notation. Two-level systems are discussed as an example, considering Stern-Gerlach interferometer. Then the Schrodinger equation and stationary states are discussed, using the free particle, the square well, barriers and the harmonic oscillator as examples. Furthermore, problems in three dimensions are discussed: spin and orbital angular momentum; the Schrodinger equation in spherical coordinates; the hydrogen atom and the addition of angular momenta.

**PC2130B Applied Quantum Physics**

Introductory aspects of quantum physics. Two state quantum systems. The wave function and Schrodinger equation. Quantum harmonic oscillator; hydrogen atom; spherical harmonics. Atomic spectra. Scattering theory. Applications such as semiconductors, lasers, quantum dots and wires.

**PC2131 Electricity and Magnetism I**

Among the four fundamental forces in nature, the electromagnetic force has great technological importance and is critical for the understanding of other subjects in science and engineering, such as optics, radiation, chemistry, biology and electrical engineering. This module provides a comprehensive treatment of electromagnetic fields and forces. It covers the following topics: vector analysis, electrostatics, special techniques in electrostatics, magnetostatics, electric and magnetic fields in matter, electromotive force, electromagnetic induction, and Maxwell's equations. This module is targeted at physics majors and science students in general.

**PC2132 Classical Mechanics**

This module aims to consider the principles of mechanics in a rigorous mathematical framework, and to establish a bridge to the principles of modern physics. The topics to be covered include: kinematics; damped and driven oscillators; energy and angular momentum, conservative forces; twobody and many-body problems, centre-of-mass; central-force motion, inverse square law, orbits, scattering; action principle; Lagrangian mechanics; Hamiltonian mechanics; small-amplitude oscillations, normal modes; rotating rigid bodies; rotating reference frames, centrifugal and Coriolis forces, Foucault's pendulum. A good command of calculus and some basic knowledge of linear algebra are required.

**PC2133 Applied Solid State Physics**

Structure of solids, practical determination of structure, elasticity, phonons and lattice vibration; thermal properties of insulators, free electron gas; semiconductor crystals. Transport properties.

**PC2134 Mathematical Methods in Physics I**

This module aims to give students the necessary mathematical skills for other physics courses. The topics to be covered include: complex numbers and hyperbolic functions; multivariable calculus; elements of vector calculus; Taylor series; Fourier series, Dirac delta-function, Fourier transforms, Laplace transforms, physical applications; second-order ordinary and partial differential equations, wave equation, diffusion equation, Poisson's equation; Green's functions; Sturm-Liouville theory; special functions associated with physical systems, Hermite polynomials, Bessel functions, Legendre functions.

**PC2193 Experimental Physics I**

This module provides a comprehensive training of both experimental and analytical skills in mechanics, thermal physics, electronics, magnetism, nuclear physics, semiconductors, optics and lasers. In particular, emphasis is placed on the measurement skill that will be required in the industries of semiconductors, optical communications and life sciences. While this module is mainly targeted at physics majors, it is also suitable for science and engineering students who are interested in a career in the above-mentioned industries.

**PC2230 Thermodynamics and Statistical Mechanics**

This module is an introductory course in statistical and thermal physics, and is a prerequisite to advanced statistical mechanics. The topics to be covered include: mathematical background, laws of thermodynamics, thermodynamics functions, chemical equilibrium and phase transitions, kinetic theory, postulates of statistical mechanics, independent particle approach of statistical mechanics, basic distributions, ideal gases, paramagnetism, equipartition theorem, etc. Science and engineering students with a background knowledge of general physics are the targeted students.

**PC2267 Biophysics I**

This module introduces the underlying principles and mechanisms of physics behind life sciences. It incorporates introductory concepts of physics into the phenomena associated with biological functions. The topics to be covered include: biological structures and the relation to biophysics; principles and methods of physics applied to biology; physical aspects of structure and functionalities of biomolecules, physical principles of bioenergy conversion and membrane-bound energy transduction; physical processes of bio-transport, nerves and bioelectricity. The module includes some basic biophysics experiments. It is targeted at both physics and non-physics students who already have basic knowledge in physics.

**SP2251 Science at the Nanoscale**

Many topics debated in nanoscience are frontier and futuristic, although some have immediate technological applications. The fundamental scientific principles of all nanotechnology applications, however, are grounded in basic physics and chemistry. This module thus aims to illustrate and discuss the physics and chemistry that are operative at the nanoscale. Students will be introduced to some fundamental principles of physics and chemistry important to the nanoscale and learn to appreciate what the world is like when things are shrunk to this scale. They will also learn about some basic physical tools that can be used to explore structures at this length scale. On completion of this module, students will learn to appreciate the linkages between the fundamental sciences and practical applications in nanotechnology.

Level |
Code |
Module |
Semester 1 |
Semester 2 |
Special Term |

3000 | PC3130 | Quantum Mechanics II | Travis Nicholson | Ng Wei Khim | |

PC3193 | Experimental Physics II | Tok Eng Soon (coord) | Tok Eng Soon (coord) | ||

PC3231 | Electricity and Magnetism II | Lim Hock Siah | |||

PC3232 | Nuclear and Particle Physics | Ng Wei Khim | |||

PC3232B | Applied Nuclear Physics | Chan Taw Kuei, Ng Wei Khim | |||

PC3233 | Atomic and Molecular Physics I | Kai Dieckmann | |||

PC3235 | Solid State Physics I | Johnson Goh | |||

PC3236 | Computational Methods in Physics | Lim Hock Siah | |||

PC3238 | Fluid Dynamics | Lim Hock | |||

PC3242 | Physics of semiconductor processing | Jeroen Van Kan, Ho Ghim Wei | |||

PC3243 | Photonics | Ji Wei | |||

PC3246 | Astrophysics I | Cindy Ng | |||

PC3247 | Modern Optics | Ji Wei | |||

PC3251 | Nanophysics | Ariando | |||

PC3267 | Biophysics II | Wang Zhisong | |||

PC3274 | Mathematical Methods in Physics II | Edward Teo | |||

PC3294 | Radiation Lab | Chan Taw Kuei | Chan Taw Kuei |

Brief Description of Modules

**PC3130 Quantum Mechanics II**

This module continues from PC2130 and completes the basic formation of the student in quantum mechanics.

Description of composite systems: tensor product, two-particle entanglement; systems of N identical particles.

Perturbation theory: time-independent, both non-degenerate and degenerate; example: Zeeman effect. Time-dependent: Fermi golden rule; example: atom in a classical e-m field. Discussion of stimulated and spontaneous emission.

Other approximation schemes: the variational principle; the WKB approximation and the “classical” region, tunneling and the connecting formula; the adiabatic approximation. Scattering: partial wave analysis and the Born approximation..

**PC3193 Experimental Physics II**

This continuous assessment module is intended to provide training in experimental techniques and analytical skills. Experiments are based on various areas of physics such as spectroscopy, nuclear physics, laser physics, optics and electronics. Some experiments involve the use of research-grade equipment like the electron microscope, the atomic force microscope and the FTIR spectrophotometer. Project-type experiments are also available. The module is targeted at science and engineering students who have a foundation in Level 2 experimental physics.

**PC3231 Electricity and Magnetism II**

This is the sequel to PC2131 Electricity & Magnetism I, leading to the objective of understanding classical electrodynamics. Most of the examples presented require a certain degree of mathematical manipulation, as compared to a first course in electricity and magnetism. It covers the following topics: conservation laws, electromagnetic waves in vacuum and in matter, guided waves, the potential formulation, Lienard-Wiechert potentials, dipole radiation, radiation from point charges, special relativity, relativistic mechanics and relativistic electrodynamics.

**PC3232 Nuclear & Particle Physics**

This is an intermediate course in nuclear physics, with an introduction to particle physics. Properties of nuclei, e.g., masses, spins, and moments, are introduced and an introductory discussion of nuclear models is presented, the semi-empirical mass formula, the Fermi gas model, the shell model and some aspects of the collective model are discussed. The energy balances and spin/parity selection rules of alpha, beta and gamma decay processes are discussed in considerable detail. The various types of interaction between radiation and matter are discussed, and an introduction to radiation detectors is given. A discussion of the operational principles and technological aspects of accelerators and an introductory survey of particle physics completes the material covered.

**PC3232B Applied Nuclear Physics**

This module explores elements of nuclear physics and its applications for students who are not physics majors, beginning with a concise introduction to the relevant elements of quantum mechanics. After a discussion of basic nuclear properties (masses, radii, spins, binding energies), elements of nuclear structure are introduced (liquid drop, Fermi gas and Shell model). Then alpha, beta and gamma decays, their selection rules and transition probabilities are discussed. The general properties of nuclear reactions, their conservation laws and energetics and the general features of the different reaction mechanisms are illustrated.The various interactions between radiation and matter are discussed, and an introduction to radiation detectors and technological applications (nuclear medicine, PET, accelerators, fusion, fission) are covered, and lastly the basics of radiation protection are discussed.

**PC3233 Atomic & Molecular Physics I**

This module presents the basic concepts and principles of atomic and molecular physics. In particular, the module revolves around the energy level schemes of atoms and molecules which are essential to the interpretation of atomic and molecular spectra. Topics covered include the hydrogen and helium atoms, spin-orbit coupling schemes, hyperfine interaction, Lamb shift, atoms in magnetic fields, multi-electron atoms, Pauli exclusion principle, Hund's rules, diatomic molecules, Born-Oppenheimer approximation, electronic, vibrational, rotational and rotational-vibrational spectra; The module is targeted at students who have background in quantum mechanics and want to build the foundations for studying the interactions of matter and light in modern atomic physics contexts.

**PC3235 Solid State Physics I**

This is a first course in solid state physics. It aims to lay the foundations for students seeking to major in physics as well as students studying in materials science and engineering. The lectures emphasize on the fundamental concepts of condensed matter, covering crystal structure and reciprocal lattice, crystal binding and elastic constants, crystal vibrations and thermal properties, free electron theory and physical properties of metals, electron in periodic potentials, and basic semiconductors. Simple model prediction data and the experimental data from real systems would be compared and discussed to help students develop an intuitive understanding of the subject.

**PC3236 Computational Methods In Physics**

The module presents basic computational methods useful for physics and science students. The lectures cover: (1) Basic numerical methods - differentiation, integration, interpolation, root-finding and random number generators, (2) Differential equations - finite difference method, shooting method and relaxation method; applications to chaotic dynamics of a driven pendulum, one-dimensional Schrödinger equation, and fast Fourier transform, (3) Matrices - Gaussian elimination scheme for a system of linear equations, eigenvalues of Hermitian matrices; Hartree-Fock approximation, (4) Monte Carlo simulations - sampling and integration; random walk and simulation of diffusion equation, stochastic differential equation, Brownian dynamics; variational Monte Carlo simulation; Metropolis algorithm and Ising model, and (5) Finite element methods - basic concepts; applications to the Poisson equation in electrostatics.

**PC3238 Fluid Dynamics**

This module introduces physics students to the fundamental aspects of fluid dynamics. The Navier-Stokes equations are derived from first principles. After a discussion of the various versions of Bernoulli's equation and the concept of vorticity, the study of fluid flows starts with the potential flows, with an application to the theory of airfoils. The theory of irrotational water waves is then presented to illustrate dispersive wave propagation and the hyperbolic tendency to form shocks. The balance of these two tendencies produces soliton solutions. The concept of flow similarity is applied to the study of boundary layer. The phenomenon of boundary layer separation is discussed. The concept of hydrodynamic instability is illustrated with the Rayleigh-Benard convection problem. The chaotic dynamics of the related Lorenz equation is then presented. A brief introduction to turbulence closes the module.

**PC3242 Physics of semiconductor processing**

The ability to create and characterize nanomaterials and nanostructures is important for many emerging advanced materials industries, from silicon electronics to intelligent nanosystems. Two general approaches to create nanostructures are bottom-up (colloidal-based chemistry) and top-down (nanofabrication and nanopatterning) methods. The course covers the essential physical chemistry principles and synthesis of bottom-up nanomaterials. Principles and practical aspects of top-down nanostructuring using nanolithography (optical, electron beam, ion beam) and pattern replication methods, including 3D-printing are discussed. Finally, nanocharacterisation using electrons, ions and scanning probe techniques are covered. Knowledge gained will be invaluable to design current and future nanosystems for diverse industries.

**PC3243 Photonics**

This module is a first course on photonics that combines fundamentals with important applications, and is targeted at students interested in modern optical technology. The course covers planar dielectric waveguides, basics of optical fibre communication, optical properties of crystals and semiconductors, interband transitions and radiative recombination, semiconductor detectors, stimulated emission and population inversion, diode laser threshold and output power, argon and YAG lasers, Q-switching and mode-locking, electro-optics modulators and flat panel displays. The course strives to maintain succinctness in physical meaning and simplicity in approach with generous allotment of numerical examples to help in understanding the equations.

**PC3246 Astrophysics** I

This module introduces the application of physics to astronomy. The students will be introduced to some astronomical phenomena, and they will learn to understand these fascinating phenomena by using basic physics. The module allows the physics students to review, and to extend their knowledge. The module cover two basic classes of celestial objects: the stars and planets. The topics include Kepler’s laws, telescopes, binary stars, stellar spectra, stellar interiors, stellar formation, and planetary tidal forces.

**PC3247 Modern Optics**

The objective of this module is to establish the interconnectedness of knowledge between principles of optics and modern sciences/technologies and identify the applications in our daily life. It covers wave properties, refraction and dispersion, interference, Michelson interferometer, Fabry-Perot cavity and optical resonator, interference filter, Fraunhofer and Fresnel diffraction, resolution limit, Fourier transformation, holography; polarisation, birefringence and wave plates, light absorption and emission, lasers. This module is targeted at physics and non-physics students, who are interested in principles of modern optics.

**PC3251 Nanophysics**

The changes to physical properties (electronic, optical and magnetic) due to formation of structures at the nanoscale will be the main emphasis of this module. Properties differing from the bulk due either to an increase in surface area/volume ratio or quantum confinement will be studied in structures ranging from quantum wells, wires and dots to self-assembled mono-layers and heterostructure formation. The kinetics and thermodynamics driving the formation of these nanostructured surfaces and interfaces will be discussed. The module will also highlight current and potential applications of these nanoscale systems. Examples of materials systems will include metals, oxides, III-V, II-VI, CNT, SiC and SiGe systems.

**PC3267 Biophysics II**

This module aims to introduce the principles and approaches of physics in the area of molecular biophysics. It includes molecular complexes of biomolecules; physical and symmetrical relationships between biomolecules; physical and structural characteristics of proteins and amino acids; symmetric and statistical descriptions of nucleic acids; first law and second law of thermodynamics in biological systems; bonding and non-bonding potentials, and stabilizing interactions in biomacromolecules, and the correlation to macromolecular structures; molecular mechanics in biological systems; bio soft condensed materials, bio-membrane and biomembrane structure, principles of molecular self assembly of biomolecules. There is a lab component included in this module. This module is targeted at both physics and non-physics students who already have basic knowledge in physics and life sciences.

**PC3274 Mathematical Methods in Physics II**

This module introduces important mathematical methods for the solution of a variety of mathematical problems in physics. The following topics are covered: functions of a complex variable, singularities and residues, contour integration; calculus of variations; transformations in physics, symmetries and group theory, discrete groups, group representations and their applications in physics; tensor analysis, application to classical mechanics, electrodynamics, and relativity.

**PC3294 Radiation Laboratory**

The module provides hands-on experience with modern detectors, electronics, data acquisition systems, radiation sources and other nuclear physics equipment that forms the basis for the applications of nuclear physics to medical physics, radiation protection and other fields. The module will be restricted to the students in the Medical Physics minor.

Level |
Code |
Module |
Semester 1 |
Semester 2 |
Special Term |

4000 | PC4228 | Device Physics for Quantum Technologies | Alex Ling | ||

PC4230 | Quantum Mechanics III | Gong Jiangbin | |||

PC4240 | Solid State Physics II | Sow Chorng Haur, Ramanathan Mahendiran | |||

PC4241 | Statistical Mechanics | George Batrouni | |||

PC4242 | Electricity and Magnetism III | Wang Qinghai | |||

PC4243 | Atomic and Molecular Physics II | Murray Barrett | |||

PC4245 | Particle Physics | Oh Choo Hiap | |||

PC4246 | Quantum Optics | Mukherjee, Manas | |||

PC4248 | General Relativity | Kenneth Hong | |||

PC4249 | Astrophysics II | Thomas Osipowicz, Abel Yang | |||

PC4253 | Thin Film Technology | Wang Xuesen | |||

PC4262 | Remote Sensing | Liew Soo Chin | |||

PC4267 | Biophysics III | Johan Van Der Maarel | |||

PC4274 | Mathematical Methods in Physics III | Kuldip Singh |

Brief Description of Modules

**PC4228 Device Physics for Quantum Technologies**

Quantum phenomena is being applied to solve practical problems in communications, sensing and information processing. These solutions take the form of new devices, collectively called quantum technology. The intention of this module is to equip the student with a working knowledge of these new devices.
We will learn how quantum technology is implemented. We place an emphasis on device physics, because without a proper understanding of the underlying science, new quantum devices cannot be developed.
We will discuss the various types of devices used over a broad range of applications covering quantum key distribution, quantum computing and quantum-limited sensing.

**PC4230 Quantum Mechanics III**

This elective module covers a range of advanced topics in Quantum Mechanics. The basics of relativistic quantum mechanics will be covered: the Klein-Gordon equation; the Dirac equation and the covariant formulation of the Dirac theory, as well as the plane wave solution of the Dirac equation, the solution of the Dirac equation for a central potential and its non-relativistic limit The rest of the module is devoted to special topics, which may include the van der Waals interaction; the behaviour of electrons in solids; masers and lasers, the EPR argument and Bell’s theorem, the interpretations of QM.

**PC4240 Solid State Physics II**

This module introduces students to elements of the physics of crystalline solids. Topics covered include: energy bands of the nearly free electron model, tight binding method, Fermi surfaces and their experimental determination, plasmons, polaritons and polarons, optical processes and excitons. We will also cover superconductivity, dielectrics and ferroelectrics, diamagnetism, paramagnetism, ferromagnetism and antiferromagnetism, and magnetic resonance. This module is targeted at physics majors, and is useful for science and engineering students who already have background knowledge of solid state physics on par with PC3235 Solid State Physics I.

**PC4241 Statistical Mechanics**

This module presents the fundamentals of statistical mechanics. Starting with the classical and quantum postulates, the three ensembles of Gibbs are derived. The statistical interpretation of thermodynamics then follows. The thermodynamic quantities are obtained in terms of the number of states, partition and grand partition functions. Applications to independent electron systems, with and without magnetic field, and Bose-Einstein condensation are given. The course ends with a brief introduction to phase transitions. This module is targeted at physics students with at least one year of thermal physics.

**PC4242 Electricity and Magnetism III**

This advanced module presents the fundamentals of classical electrodynamics in much depth. It covers the following topics: relativistic formulation of the electromagnetic field, covariance of electrodynamics, conservation laws, radiation by moving charges, Lienard-Wiechert potentials, Larmor's formula, angular distribution of radiation, spectral properties of radiation, Cherenkov radiation, Bremsstrahlung, synchrotron radiation, multipole expansions, and applications. A good mathematical foundation is required.

**PC4243 Atomic & Molecular Physics II**

The objective of this module is to provide students with a background to the important developments in atomic physics over the last 30 years that have now become standard techniques utilized in many laboratories around the world. The lectures provide a detailed description of the interaction of atoms with electromagnetic fields and applies this analysis to a number of applications such as laser spectroscopy, laser cooling, and magnetic and optical trapping. The course will provide students with a comprehensive background to the tools of modern atomic physics

**PC4245 Particle Physics**

This is an introductory course on the fundamental constituents of matter and their basic interactions; important concepts and principles, recent important experiments, underlying theoretical tools and calculation techniques in elementary particles physics will be expounded. The topics covered are: basic properties of elementary particles and the standard model, relativistic kinematics; symmetries: isospin and SU(3), quark model; parity and CP violation; Feynman diagrams and rules; quantum electrodynamics; cross sections and lifetimes: deep inelastic scattering; and introductory gauge theories and unified models. This module is mainly targeted at physics majors.

**PC4246 Quantum Optics**

This module is an introduction to the quantum description of the electromagnetic field, with a special focus on phenomena at optical frequencies; in short, "quantum optics". It starts with two introductory chapters: a concise reminder of important facts and devices of classical optics; and a presentation of typical quantum phenomena that have been observed with light (entanglement, violation of Bell's inequalities, teleportation…). The core of the module is the canonical quantization of the electromagnetic field and the introduction of the corresponding vector space ("Fock space") and field operators. Then, we present the main families of states (number, thermal, coherent, squeezed) and the most typical measurement techniques (photo-detection, homodyne measurement, first- and second-order coherence, Hong-Ou-\Mandel bunching). The statistical nature of light fields is highlighted. Finally, we present the basic case studies of photon-atom interactions in the full quantum approach: cavity quantum electrodynamics (Janyes-Cummings model), spontaneous decay (Wigner-Weisskopf approach).

**PC4248 General Relativity**

This module provides an introduction to the theory of general relativity. The topics covered are: general tensor analysis, the Riemann tensor, the gravitational field equation, the Schwarzschild solution, experimental tests of general relativity, black holes, and Friedmann-Robertson-Walker models of the expanding universe. While this module is mainly targeted at physics majors, it is also suitable for science students with a strong mathematical foundation.

**PC4249 Astrophysics II**

Starting with an introduction to the nuclear physics of stars and the processes of nucleosynthesis, following a brief introduction to nuclear physics. nucleosynthesis via quiescent burning, and the processes that lead to the production of heavy (A>60) elements are covered. The endstages (brown dwarfs, white dwarfs, neutron stars and black holes) are discussed in detail. In the second part of the module, large structures in the universe, are discussed, including star clusters, galaxy structure, and galaxy clustering. The module ends with a discussion of the cosmological scale structure of the universe. This module is a continuation of PC3246 Astrophysics I.

**PC4253 Thin Film Technology**

The scope of the course embraces the basic principles of thin-film deposition techniques such as chemical vapor deposition and physical vapor deposition as well as their applications in the microelectronics industry. The basic principles include vacuum technology, gas kinetics, adsorption, surface diffusion and nucleation. These are the fundamental features which determine the film growth and the ultimate film properties. Common thin-film characterization methods which measure film composition and structure as well as mechanical and electrical properties are also covered. This course is for senior physics students with an interest in pursuing a career in industry.

**PC4262 Remote Sensing**

This module explores the physics behind the chain of events that leads to the acquisition of remote sensing images. Topics covered include: satellite orbital dynamics, radiometry, scattering of EM waves, radiative transfer in the atmosphere, ocean and vegetation canopy, various types of sensors, and examples of remote sensing applications. Skills in image processing and analysis of remote sensing images will be gained through project works. This module is targeted at students who are interested in applying physics to real-life situations. The students should already have a basic knowledge of physics and mathematical methods.

**PC4267 Biophysics III**

This module covers the principles of statistics in relation to biophysics and bio soft materials. It focuses on: modeling of biomacromolecular structure and statistical complexities; molecular mechanics of biomolecules; statistical models for structural transitions in biopolymers, statistical physical description of structural transitions in macromolecules, simulation of macromolecular structure, structural transitions in polypeptides and proteins; coil-helix transitions; prediction of protein secondary and tertiary structures; statistics of structural transitions in polynucleotides and DNA; modeling of non-regular structures of biomacromolecules. This module is targeted at both physics and non-physics students who already have basic knowledge in physics, thermodynamics and molecular biology.

**PC4274 Mathematical Methods in Physics III**

This module introduces advanced mathematical methods that are essential in many areas of theoretical physics. The topics covered are: differentiable manifolds, curved manifolds, tangent and dual spaces, calculus of differential forms, Stokes' theorem, and applications to electromagnetic theory; symmetries of manifolds, Lie derivatives, Lie groups and algebras, their representations and physical applications. The module is targeted at students who wish to study theoretical physics.

Level |
Code |
Module |
Semester 1 |
Semester 2 |
Special Term |

5000 | PC5198 | Graduate Seminar Module in Physics | Thomas Osipowicz | ||

PC5201 | Advanced Quantum Mechanics | Edward Teo | |||

PC5202 | Advanced Statistical Mechanics | Wang Jian Sheng | |||

PC5204 | Special Topics in Physics: Magnetic Materials and Applications | Ramanathan, Mahendiran | |||

PC5204A | Special Topics in Physics: Soft Materials and Flexible Devices | Liu Xiang Yang | |||

PC5204B | Special Topics in Physics: Analytic Approximations | Wang Qinghai | |||

PC5205 | Topics in Surface Physics | Wang Xuesen | |||

PC5206 | Selected Topics in Quantum Field Theory | Wang Qinghai | |||

PC5209 | Accelerator Based Materials Characterisation | Chan Taw Kuei | |||

PC5210 | Advanced Dynamics | Gong Jiangbin | |||

PC5212 | Physics of Nanostructures | Feng Yuan Ping | |||

PC5213 | Advanced Biophysics | Yan Jie, Artem Efremov | |||

PC5214 | Principles of Experimental Physics | Christian Kurtsiefer | |||

PC5215 | Numerical Recipes with Applications | Wang Jian Sheng | |||

PC5216 | Advanced Atomic and Molecular Physics | Kai Dieckmann | |||

PC5228 | Quantum Information and Computation | Dagomir Kaszlikowksi | |||

PC5239B | Special Problems in Physics: Variational techniques | Berge Englert | |||

PC5247 | Photonics II | Li Wenhui | |||

QT5198 | Graduate Seminar in Quantum Information | Murray Barrett | |||

QT5201M | Quantum State Estimation | Berthold-Georg Englert | |||

QT5201S | Quantum Electronics | Christian Kurtsiefer |

Brief Description of Modules

**PC5198 Graduate Seminar Module in Physics**

This is a required module for all research Masters and PhD students admitted from AY2004/2005. The main purpose of this module is to help graduate students to improve their presentation skills and to participate in scientific seminars/exchanges in a professional manner. The activities of this module include giving presentations during the lecture hours and attending seminars organised by the Department. Students are also required to write summaries of some departmental seminars attended. The grade of this module will be "Satisfactory/Unsatisfactory" based on student's talk presentations, participation of seminars and the summary writing.

**PC5201 Advanced Quantum Mechanics**

This module is an introduction to advanced topics in quantum theory. Topics include applications in many-body systems; Scattering theory; Approximation methods and their applications. General description of relativistic equations and their solutions; Interaction with electromagnetic fields; Path integral formulation of quantum mechanics. This module is targeted at all students undertaking graduate studies.

**PC5202 Advanced Statistical Mechanics**

This module presents an introduction to phase transitions and fluctuations. For phase transitions, the course starts with the treatment of Landau and mean field. Exact Ising model results are then discussed. Critical exponents are introduced and their relations obtained using the scaling hypothesis and Kadanoff's scheme. Real space renormalization is then used to show how the critical exponents can be calculated. For fluctuations, Langevin, Fokker-Planck equations will be used. Time dependence and fluctuation dissipation theorem then follow. Brownian motion will be used as an example. This module is targeted at physics graduate students with at least one year of statistical mechanics.

**PC5204 Special Topics in Physics: Magnetic Materials and Applications**

This module presents special selected topics of current interest. For this academic year, the module aims to introduce novel magnetic phenomena in solids with emphasis on physics and applications of spin based electronics or spintronics. The topics covered include general introduction to magnetism, exchange interactions in magnetic solids, band structure, half metals, dilute magnetic semiconductors, spin dependent electrical transport, spin polarization & detection, magneto transport in multilayers, oxides & magnetic semiconductors, magnetic nanostructures and spin injection across various interfaces. Other spin dependent phenomena such as magneto caloric, magneto elastic, magneto impedance and magnetic resonance effects will also be discussed. Application of spintronics in novel devices including GMR read heads, MRAM, spinFET, spin transistor, magnetic sensors for strain & bio-molecule detection will be illustrated. This module is targeted at postgraduate students of physics, engineering and materials science who have basic knowledge in magnetism and solid state physics/devices.

**PC5204A Special Topics in Physics: Soft Materials and Flexible Devices**

Flexible electronics/devices and integrating various flexible electronics, sensors, and energy harvesting devices, etc. into fabrics have been attracting considerable interests in many areas due to the great potential applications in the smart, living, health care and medication. What makes them so different? In this module, we will explore the latest break-through in materials, flexible devices design and fabrication. It also potential applications and future perspectives. The module will combine the seminars with projects, and lecturing with classroom discussion.

**PC5204B Special Topics in Physics: Analytic Approximations**

This module covers advanced mathematical methods for obtaining approximate analytical solutions to physical problems. It is designed to help graduate students build the skills necessary to analyse equations, integrals, and series that they encounter in their research. Topics include local analysis of differential equations, asymptotic expansion of integrals, and summation of series.

**PC5205 Topics in Surface Physics**

Selected topics from the following will be covered: introduction to surfaces in ultrahigh vacuum; thermodynamic and statistical properties of clean surfaces; interactions between light/ion/electron beams with surface and the surface analysis techniques derived from (including XPS, UPS, IR/Raman, RBS, SIMS, Auger, STM/AFM etc.); electronic, magnetic and optical properties at the surface; surface science in thin films, nanostructures and biomaterials; adsorption phenomena at surfaces; surface processes on nucleation and epitaxial growth; catalysis etc. There are laboratory sessions in this module which contains practice on XPS, SIMS, STM/AFM and IR. This module is targeted at physics, chemistry, materials science and engineering students who already have a basic knowledge of solid-state physics.

**PC5206 Selected Topics in Quantum Field Theory**

This is an advanced module for students of theoretical physics. The topics covered are: Second quantization and path integral formulation of quantum field theory, Feynman rules for scalar, spinor, and vector fields, renormalization and symmetry, renormalization group, and connection with condensed matter physics.

**PC5209 Accelerator Based Materials Characterisation**

The course gives an introduction to the physics of ion beam analysis. After a general introduction, inter-atomic potentials, cross sections and stopping powers are discussed, and the theory of the stopping process is developed based on the Thomas-Fermi statistical atom. Accelerators and other instrumentation are introduced, and a range of analytical techniques is discussed in detail: Rutherford Backscattering (RBS), Proton Induced X-ray Emission (PIXE), Elastic Recoil Detection Analysis (ERDA), Nuclear Reaction Analysis NRA, and Accelerator Mass Spectrometry (AMS). Finally, the more specialised fields of Nuclear Microscopy and Synchrotron radiation are discussed.

**PC5210 Advanced Dynamics**

The module aims to understand Lagrangian mechanics, Hamiltonian mechanics, and basic ideas of nonlinear dynamics and chaos. Topics discussed are: variational principle and Lagrangian mechanics, Hamiltonian mechanics, the Hamiltonian formulation of relativistic mechanics, symplectic approach to canonical transformation, Poisson brackets and other canonical invariants, Liouville theorem, the Hamilton-Jacobi equation, Hamilton's characteristic function, action-angle variables, integrable systems, transition from a discrete to continuous system, relativistic field theory, Noether's theorem, Lie groups and group actions, Poisson manifolds, Hamiltonian vector fields, properties of the Hamiltonian fields, conservative chaos, the Poincare surface of section, KAM theorem, Poincare-Birkhoff theorem, Lyapunov exponents, global chaos, effects of double dissipation and fractals.

**PC5212 Physics of Nanostructures**

The module provides an introduction to the scientific foundations of the function, fabrication and characterization of nano-structured materials and nano-devices. The topics covered are: reviews of quantum mechanics in reduced dimensions and solid state physics, common techniques for nano-structure fabrication and characterization, transport in low-D systems, optoelectronics of nanostructures, nanotubes and nanowires, clusters and nano-crystallites, molecular electronics, magnetic nano-structures. This module is designed for postgraduate students who are interested in nanoscience and nanotechnology research and applications.

**PC5213 Advanced Biophysics**

This module focuses on theories and techniques used in some important areas of biophysics and life sciences. The topics covered are: quantum mechanical approach of light and transition; absorption spectroscopy; linear and circular dichroism of biological molecules; emission spectroscopy, fluorescence spectroscopy and applications to biomacromolecules; NMR; equilibria of macromolecular solutions; biomembrane structure and transport of macromolecules and transport across biomembranes; kinetics and techniques of protein crystallization; biomineralization/demineralization in human body. This module also includes a lab component. This module is targeted at both physics and non-physics students who already have a basic knowledge in physics, thermodynamics and molecular biology.

**PC5214 Principles of Experimental Physics**

This module provides experimental knowledge on techniques used in modern optical and atomic physics. The focus is on practical implementation of optical measurement methods, and the corresponding technology. Areas covered are practical photodetection, lock-in signal recovery, simple feedback systems, FPI cavities, optical thin films, basic vacuum systems, manipulation of cold atoms, and aspects of working at low temperatures (below 77K). The module will have a strong focus in practical techniques, targeting students who intend to work in the area of atomic, molecular, ion and optical or cryogenic physics.

**PC5215 Numerical Recipes with Applications**

Covers computational techniques for the solution of problems arising in physics and engineering, with an emphasis on molecular simulation and modelling. Topics will be from the text, ?Numerical Recipes?, Press et al, supplemented with examples in materials and condensed matter physics. This course insures that graduate students intending to do research in computational physics will have sufficient background in computational methods and programming experience.

**PC5216 Advanced Atomic and Molecular Physics**

This module introduces from an experimentalists point of view to the modern world of ultracold quantum gases that so much changed atomic physics in the past two decades. The lectures present the basic experimental methods of laser cooling, magnetic and optical trapping, and evaporative cooling that produce matter near absolute zero temperature. We then discuss basic effects like Bose-Einstein condensation and Pauli pressure. Further, selected research examples are presented that give insight to some of the many close relations between quantum matter designed in many labs worldwide and other physical systems found in the range of quantum information science, condensed matter physics, metrology, nuclear physics, and astronomy. Solid background in quantum mechanics, atomic physics, and statistical mechanics is desired.

**PC5228 Quantum Information and Computation**

The module will provide an introduction to the physics and mathematics of quantum information in general and quantum computation in particular. In addition to physics majors, the course addresses students with a good background in discrete mathematics or computer science.The following topics will be covered: (1) Introduction: a brief review of basic notions of information science (Shannon entropy, channel capacity) and of basic quantum kinematics with emphasis on the description of multi-qubit systems and their discrete dynamics. (2) Quantum information: Entanglement and its numerical measures, separability of multi-partite states, quantum channels, standard protocols for quantum cryptography and entanglement purification, physical implementations. And (3) Quantum computation: single-qubit gates, two-qubit gates and their physical realization in optical networks, ion traps, quantum dots, Universality theorem, quantum networks and their design, simple quantum algorithms (Jozsa-Deutsch decision algorithm, Grover search algorithm, Shor factorization algorithm).

**PC5239B Special Problems in Physics: Variational techniques**

This module will present a unified look at the basic branches of physics (classical mechanics, quantum mechanics, electrodynamics, thermodynamics and statistical physics) from the perspective of variational principles, which offer compact statements of the fundamental laws and are also an important tool for designing models and finding approximate solutions.

**PC5247 Photonics II**

The module is intended to provide detailed treatment of the principles of lasers and working knowledge of major optical techniques used in manipulating laser spatial mode properties and their temporal and spectral characteristics. The topics being covered include laser beams, laser theory, laser survey, modulation techniques, non-linear optics, and fiber optics.

**QT5198** **Graduate Seminar in Quantum Information**

The graduate seminar module will introduce current topics in quantum information science with an emphasis on recent research results. A balanced discussion of both theoretical and experimental topics will provide an opportunity to discuss in detail the main techniques and overall trends in the broad field of quantum information.

**QT5201M: Quantum State Estimation**

This course will introduce graduate students in NUS to the concepts and methods of quantum state estimation, and thereby enable them to draw inference from data acquired in quantum experiments. Students will learn the principles of quantum state estimation, and how to apply the concepts and methods in practical situations.

**QT5201S: Quantum Electronics**

In this module, basic electronic techniques related to quantum technologies are introduced at a level that allows students to analyze, design, build and modify electronics encountered in experimental work on quantum technologies. It covers basic circuit design, with a focus on techniques related to typical signal conditioning and processing tasks encountered in experiments and application engineering involving quantum systems like single photon detection and generation, atom and ion traps, laser spectroscopy, optical modulators and some radio-frequency techniques to drive atomic transitions, and electronic techniques at cryogenic temperatures.