## Course Information

# Physics and Applied Physics Courses

- Year 1 — Year 3 Courses
- Year 4 Courses | Graduate Level Courses
- Projects and Internships | Legacy Projects and Internships
- Physics Courses For Non-Physics Majors
- Unrestricted Electives

## Year 1 — Year 3 Courses

Basic concepts in optics and wave phenomena, such as the modelling of vibrations and waves, rays, interference, and diffraction.

*Prerequisite: Physics and Maths at A or H2 level, or equivalents.**Not available to students who have taken/are taking EE1002.*

Key ideas of fields and oscillations, in the context of electrostatics, magnetism, simple harmonic motion and electric circuits.

*Prerequisite: Physics and Maths at A or H2 level, or equivalents.**Not available to students who have taken/are taking PH1011, PH1012, PH1802, EE1002, PHYS1B, CY1302, or CY1306.*

Basic concepts and problem solving skills for analysing objects moving close to the speed of light and particles exhibiting quantum behaviour.

*Prerequisite: Physics and Maths at A or H2 level, or equivalents.**Not available to students who have taken/are taking CY1307.*

Basic laboratory course in experimental physics, with experiments in mechanics, basic optics and thermal physics. The laboratory sessions provide an active learning experience for appreciating key physics concepts. Students also learn about data acquisition, error analysis, error distribution, and data analysis.

*Prerequisite: Physics at A or H2 level or equivalent.*

Basic laboratory course in experimental physics, with experiments in electricity and magnetism, circuits, optics and wave phenomena. The laboratory sessions provide an active learning experience for appreciating key physics concepts. Students also learn about data acquisition, error analysis, error distribution, and data analysis.

*Prerequisite: Physics at A or H2 level or equivalent.*

Introduction to quantum mechanics. The formalism of quantum mechanics is developed in terms of matrices and wave functions, along with details about foundational quantum experiments and real-life applications.

*Prerequisites: (MH1801 and PH1107) OR (MH1801 and CY1307) OR (MH1802 and MH1803 and PH1107) OR (CY1307 and CY1601 and CY1602) OR (MH1101 and MH1200 and PH1107).**Not available to students who have taken/are taking CY1303.*

Fundamental principles of electromagnetism. Students also learn analytical, computational and mathematical skills involved in solving partial differential equations, and how to interpret the physical concepts behind the equations and their solutions.

*Prerequisites: (MH1801 and MH2800 and PH1106) OR (MH1802 and MH1803 and MH2802 and PH1106) OR (CY1601 and CY1602 and CY1308) OR (MH1101 and MH1200 and PH1106).*

Basic concepts and problem solving skills for analytical mechanics. The physical intuition and analytical skills covered in this course are essential for advanced topics such as quantum mechanics and photonics.

*Prerequisites: (MH2800 and PH1104) OR (MH1803 and MH2802 and PH1104) OR (CY1601 and CY1602 and CY1308)**Not available to students who have taken/are taking MA1001.*

Intermediate laboratory course in experimental physics, with experiments involving electronic signal processing, interferometry, spectroscopy, and more.

*Prerequisite: PH1198 or CY1400.*

Intermediate laboratory course in experimental physics, with experiments involving computer-aided data acquisition, spectroscopy, thermal physics, and more.

*Prerequisite: PH1199 or CY1400.*

Concepts in physical optics and electromagnetic wave phenomena, including the phenomena of polarisation, interference and diffraction.

*Prerequisite: PH1105*

Introduction to lasers and their working principles, including stimulated emission of radiation, atomic transitions, rate equations, coherent optical oscillations, laser resonators, and design principles for laser devices.

*Prerequisite: PH1105.*

Intermediate course in quantum mechanics, featuring the logical and systematic development of quantum mechanical formalism. Topics include quantum kinematics, finite- and infinite-dimensional systems, quantum measurements, symmetries in quantum mechanics, angular momentum, hydrogenic atoms, and perturbation theory.

Postulates and key ideas in statistical mechanics, with applications to classical and quantum gases. Topics include the postulates of statistical mechanics, temperature and entropy, density of states and heat capacity in black body radiation, ideal classical gases, free electron gases, phonons, and phase transitions.

*Prerequisite: PH3101.*

Introduction to atomic physics and the quantum mechanical properties of atoms. The fundamental concepts taught here are applicable to condensed matter physics, nuclear physics, and molecular physics.

*Prerequisite: PH3101.*

Introduction to cosmology, covering topics such as inflation theory, structure formation, the cosmic microwave background, gravitational waves, the geometry of the universe, and open problems in cosmology such as dark matter, dark energy and primordial gravitational waves.

Interdisciplinary course covering a rapidly growing cross-disciplinary research frontier between physics, information science and computation. Students will be introduced to the fundamentals of classical and quantum information science, including topics in information physics, quantum information, and quantum computation.

*Prerequisites: (PH2101 and MH1402) OR (PH2101 and MH2802) OR (CZ1016 and MH2802) OR (CY1602 and CY1307)*

Introduction of basic formalism and interpretation of decoherence of open quantum systems, so students have a more complete understanding of the philosophical, mathematical and experimental foundations of quantum mechanical phenomena. It applies the mathematical formalisms to describe contemporary experiments in quantum computing, and explores the role decoherence plays in interpretations of quantum mechanics.

*Prer**equisites: **PH3101** *

The physics of fluid motion. Topics include equations of flow, compressible and incompressible fluids, and dynamical phenomena in fluids.

*Prerequisite: PH2104.*

Basic concepts of determinism and randomness in the physical world. Topics include dynamical system theory, and the computational and analytical methods for studying chaotic and nonlinear systems.

*Prerequisite: PH2104.*

Principles and techniques for fabricating micro- and nano-electronic devices. Topics include semiconductor-based device fabrication and magnetic, organic and bioMEMS devices.

*Prerequisite: PH2102*

Introduction to how physics approaches living matter. Topics include molecular biophysics, structural biology, and common biophysical methods used to investigate the structure and dynamics of biomolecules.

*Prerequisite: PH2103.*

## Year 4 Courses

Note: not all Year 4 courses are offered yearly. “Even AYs” refers to academic years (AYs) beginning in an even calendar year (e.g., AY2020/2021). “Odd AYs” refers to AYs beginning in an odd calendar year (e.g., AY2021/2022). For example, an “Even AY” Semester 2 course will be offered in AY2020/2021, even though the Semester 2 instruction period takes place in an odd calendar year (2021).

###### PH4401

Quantum Mechanics III

4 AU | Not offered

Register for PH7042 instead

Advanced concepts in quantum mechanics, with a focus on the quantum behavior of multi-particle systems. Topics include scattering theory, quantum entanglement, and the creation and annihlation of particles. The analytical and numerical methods taught in this course provide the theoretical background for advanced courses in quantum field theory, high energy physics, and condensed matter physics.

*Prerequisite: PH3101.This course is no longer offered. Interested students should instead register for PAP777 (Graduate Quantum Mechanics).*

Key concepts in surface and interface science, with a focus on electronic structures. Topics include the thermodynamics of surface phenomena, Schottky barriers and band offsets in semiconductors, band engineering, and analytical techniques such as scanning tunneling microscopy and photoemission.

*Prerequisite: PH3102.*

How quantum mechanical behavior emerges in condensed matter systems at the nanometer scale. This course provides an overview of nanoscale phenomena that can be observed experimentally, and the analytical skills for describing them. Students will acquire the knowledge required to follow or perform research in applied nanoscience and technology.

The structure of nuclei and their properties. Topics include the properties of nuclei, nuclear structure, selection rules for alpha, beta and gamma decay processes, nuclear lifetimes, and nuclear reactors and nuclear power.

*Prerequisite: PH3101*

Approaches to economics and finance inspired by statistical physics. Topics include basic concepts in probability and statistics, Gaussian and fat-tailed return distributions, time series, random matrix theory, correlation filtering and minimal spanning trees, and agent-based models of financial markets.

Survey of particle physics for advanced undergraduates and beginning graduate students. Topics include the Standard Model of quarks, leptons and the fundamental interactions, tests of conservation laws, probes of physics beyond the Standard Model, experimental techniques in particle physics, and current and future experimental challenges.

*Prerequisite: division approval.*

Use of computational methods for studying complex physical situations, such as multi-dimensional systems, nonlinear phenomena, and stochastic phenomena. Emphasis is placed on practical analysis, problem-solving, and debugging skills, which are developed through programming assignments involving problems in electromagnetism, quantum mechanics, and statistical mechanics.

*Prerequisite: PH3101.*

Advanced course in statistical mechanics and its applications to complex physical systems. Topics include thermodynamic systems in equilibrium, entropy, thermodynamic ensembles, the equipartition theorem, Fermi-Dirac and Bose-Einstein statistics, quantum fluids, and the properties of classical liquids.

Advanced course in the dynamics of electromagnetic fields. Topics include advanced techniques in vector calculus, the description of electrodynamic phenomena using Lorentz covariant tensors, and gauge theories.

*Prerequisite: PH2102.*

Special course in theoretical physics. Currently not offered.

*Prerequisite: division approval.*

Introduction to the quantum theory of fields. Topics include the basic methods of quantum field theory and its applications to particle physics to many-body problems in condensed matter physics.

*Prerequisite: PH3101.*

Special course in theoretical physics. Currently not offered.

*Prerequisite: division approval.*

Introduction to solid state devices, with an emphasis on the modern microelectronics industry. Topics include the electronic band structures of semiconductors, defects, the drift, diffusion and recombination of charge carriers, p-n junctions, diodes, and magnetic devices.

*Prerequisite: PH3102.*

Introduction to the physics of soft matter, such as colloids, foams, granular media and liquid crystals. The course will cover both the theoretical concepts and the experimental methods used to develop and study soft matter.

*Prerequisite: PH2103.*

Special course in applied physics. Currently not offered.

*Prerequisite: division approval.*

Fundamentals of radiation physics, with a focus on clinical applications. Topics include the basic concepts and techniques of dosimetry, treatment planning, radiobiology, radiotherapy, and radiation safety.

*Prerequisite: PH3101*

Introduction to cutting-edge biosensing and bioimaging techniques. This course emphasises how basic physics principles are applied to instruments for biosensing and imaging, and implications for the treatment of medical problems.

*Prerequisite: PH2301 or CM3041.*

The physics of plasmonic devices and metamaterials, which are used to manipulate electromagnetic waves at nanometer length scales. The course emphasises state-of-the-art developments at the intersection of photonics, solid state physics, and spectroscopy.

*Prerequisite: PH2102.*

Special course in applied physics. Currently not offered.

*Prerequisite: division approval.*

An introduction to the physics of phase transitions. Topics covered include scaling; critical exponents; universality; fractal behavior; transfer matrix; Monte Carlo simulations; renormalization group.

Advanced concepts and problem solving skills in condensed matter physics. Topics covered include Second Quantization; Electrons in a lattice; Mean Field Theory; Linear Response Theory; Topology in condensed matter.

Unified macroscopic theory of the dynamics of classical electromagnetic waves, in accordance with the form invariance of the Maxwell equations and the constitutive relations. Topics covered include fundamental importance of the k vector in electromagnetic wave theory; Media; Reflection and Guidance; Radiation; Theorems; Relativity.

Basic concepts of determinism and randomness in the physical world. Topics covered include Linear Dynamical System; Ingredients of a Dynamical System; Stability Properties of Linear Dynamical System; Phase Portraits from the Stability Properties of Manifolds of Fixed Points in Continuous-Time Nonlinear Dynamical System; Bifurcations; Lorenz Equations; Nonlinear Mapping and their Dynamical Properties; Fractals.

State-of-the-art optical spectroscopic and imaging techniques for non-destructive materials characterization, with widespread use in the study of conventional bulk and thin films as well as nanoparticles, nano-devices and bio-molecular systems. Topics covered include reflection and transmission spectroscopy; Fourier transform infrared spectroscopy; Raman scattering; photoluminescence; ultrafast spectroscopy; a brief introduction to nonlinear optics and the basics of lasers.

Fundamental concept and principles of key topics in advanced optics and nonlinear optics. Mechanisms of beam manipulation, generation of ultrafast laser pulses, optical resonators, wavelength conversion, nonlinear absorption etc.

Central theoretical framework and tools which are paramount to understanding the advantage brought by quantum information processing and some experimental basics of realizing these technologies.

Advanced topics in quantum mechanics. Topics covered include scattering theory; resonances; quantum entanglement; the Einstein-Podolsky-Rosen paradox and Bell's inequalities; fermions and bosons; second quantization; principles of quantum field theory; and quantum electrodynamics.

## Projects and Internships

The following modules are available for students admitted in 2016 or later, for the completion of their Final Year Project and internship/attachment degree requirements.

Two-semester research project, supervised by a faculty member, culminating in a thesis report and a seminar presentation.

*Prerequisites: 12 AU of PH3XXX courses.**Not available to students who have taken/are taking the 22-week internship (PH4417). For students admitted 2019 or later, the Final Year Project is PH4421.*

Twenty-two week internship in an approved company or institution.

*Prerequisites: PH1104, PH1105, PH1106, PH1107, PH1198, PH1199, PH2101, PH2102, PH2103, PH2104, PH2198, PH2199, PH3101, and PH3102; or by permission.**Not available to students who have taken/are taking PH4416 or other internship modules, or the Final Year Project (PH4415 or PH4421).*

Twenty-week internship in an approved company or institution.

*Prerequisites: PH1104, PH1105, PH1106, PH1107, PH1198, PH1199, PH2101, PH2102, PH2103, PH2104, PH2198, PH2199, PH3101, and PH3102; or by permission.**Not available to students who have taken/are taking PH4416 or other internship modules, or the Final Year Project (PH4415 or PH4421), or PH4703 OEP6, PH4704 OEP6, PH4900, or PH4901.*

Two-semester research project, supervised by a faculty member, culminating in a thesis report and a seminar presentation.

*Prerequisites: 12 AUs of PH3XXX courses.**Not available to students who have taken/are taking PH4417 or other internship module, or the Final Year Project (PH4415 or PH4421), or PH4701, OEP12, PH4702 OEP12, PH4703 OEP6, PH4704 OEP6, PH4900, or PH4901.*

6-month internship with a startup company, located in a major global innovation hub (remote internship can be arranged if there are travel restrictions).

The Overseas Entrepreneurship Programme (OEP) allows entrepreneurially inclined students to intern at a startup company, so as to experience the process and challenges that entrepreneurs face in building and growing their companies. The startup companies are located in major global innovation hubs such as Silicon Valley, New York, Shanghai and Berlin. Students can also opt to work for a startup company that is based in Singapore, but with ambitions to grow their business globally.

Two-semester research project, supervised by a faculty member, culminating in a thesis report and a seminar presentation.

Ten-week attachment in an approved company or institution.

Twenty-two week internship in an approved company or institution.

This course teaches the basic concepts and problem solving skills in Mechanics, Thermal Physics and Electricity & Magnetism. You will develop physical intuition and analytical skills which are important for studying physical systems and solving problems in these areas of Physics.

*Prerequisite: Physics at A or H2 level, or equivalent.**Not available to students who have taken/are taking CY1305, CY1306, FE1001, FE1011, IM1091, MS1001, PH1012, PH1104, PH1106, or PH116S.**This course is also offered as a GER-PE (STS).*

This course teaches basic concepts and problem solving skills in Mechanics, Thermal Physics and Electricity & Magnetism. You will develop physical intuition and analytical skills which are important for studying physical systems and solving problems in these areas of Physics.

*Not available to students who have taken/are taking CY1305, CY1306, FE1001, FE1011, FE1012, IM1090, PH1011, PH1104, PH1106, or PH116S.**This course is also offered as a GER-PE (STS).*

Fundamentals of physics, with an emphasis on practical applications in engineering, the biomedical sciences, and other fields. Students also learn how to read scientific material effectively, identify fundamental concepts, reason through scientific questions, and solve quantitative problems. Topics covered include mechanics, wave motion, and thermodynamics.

*Prerequisite: mathematics at the A or H2 level, or equivalent.**Not available to students who have taken/are taking PH1104.*

Fundamentals of physics, with an emphasis on practical applications in engineering, the biomedical sciences, and other fields. Topics covered include electricity and magnetism, optics, and modern physics.

*Prerequisite: PH1801.**Not available to students who have taken/are taking PH1106. For CBC students, this course may be replaced with PH1106.*

Basic concepts and applications of electronic elements and circuits. Topics include analog and digital electronics, tools for circuit design and board layout, and typical circuits for scientific instrumentation. The course includes laboratory sessions providing hands-on experiments with various prototype circuits, and a project to design and realize a simple electronic device.

Introduction to physics research, supervised by a faculty member. Suitable for undergradautes from year 2 onwards. Research topics are determined by the faculty supervisors.

*Prerequisite: division approval.*

Introduction to physics research, supervised by a faculty member. Suitable for undergradautes from year 3 onwards. Research topics are determined by the faculty supervisors.

*Prerequisite: Division approval.*

Introduction to useful technological skills including computer-controlled electronics, 3D printing, and techniques for building basic equipment and products related to Science and Technology.

*This course is also offered as Major Prescribed Elective for Applied Physics students.*

Introduction to useful technological skills including computer simulation, prototyping with 3D printing, and other techniques for building basic equipment and products related to Science and Technology.

*Prerequisite: School approval**This course also offered as a Major Prescribed Elective for Applied Physics students.*