Open to juniors and seniors majoring in physics and astronomy department. Amateur radio for middle-school science teaching. Fundamentals of electromagnetic waves and propagation, the ionosphere and space weather. Basic electronics, antenna design and safety. Provides information necessary to gain the technical level of ham radio license. Plasma physics of the earth's magnetosphere, including interactions of the magnetosphere with the solar wind and the ionosphere.

The emphasis is on large-scale phenomenon, but small scale kinetic physics is discussed in cases where it affects the large-scale phenomena. Survey of analytical methods used by research physicists and astronomers. Includes complex variables, ordinary differential equations, infinite series, evaluation of integrals, integral transforms, normal-mode analysis, special functions, partial differential equations, eigen functions, Green's functions, and variational calculus.

Requires completion of project using a low-level programming language. Graduate level course on non-relativistic quantum mechanics. Topics include early quantum theory, one-dimensional systems, matrix formulation, quantum dynamics, symmetries and conservation laws, bound states, scattering, spin, and identical particles, perturbation theory. Maxwell's equations, wave propagation, special relativity and covariant formulation, charged-particle dynamics, and radiation. Physics of structures and devices at the nanometer scale. After are view of solid state physics, topics include nanostructured materials, nanoelectronics, and nanomagnetism.

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- Group of Quantum Optics (GOQ)!
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Emphasis on relevance of nanophysics to current and future technologies. Topics include nanomechanics, bionanotechnology, advanced sensors and photonics. Study of crystals by x-ray, electron and neutron diffraction. Includes basic diffraction theory as well as methods for characterizing the structure, composition and stresses in crystalline materials. Required for undergraduate materials science and engineering majors.

Cross-list: MSCI This two-semester course will familiarize students with basic experimental techniques that are common to all academic and industrial research laboratories. Topics will include lab safety, mechanical design, computer-based data acquisition and experimental control, laboratory electronics, vacuum technology, optics, thermal measurement and control, cryogenics and charged particle optics.

Introduction to study and creation of nanoscale structures, emphasizing relevant physical principles. Techniques covered include optical, X-ray, electron-based and scanned-probe characterization, as well as patterning, deposition and removal of material. Radiation processes and their applications to astrophysical phenomena and space science. The course treats radiative transfer, radiation from moving charges, relativistic covariance and kinematics, bremsstrahlung, synchrotron radiation, Compton scattering, some plasma effects, and radiative transitions in atoms and molecules.

Introduction to biological physics. Review of basic physical concepts. Cells and their components. Diffusion and random walks. Entropy and energy concepts and their roles in biological systems. Modern experimental methods. Applications to biological macromolecules. This is an introductory course for physical sciences graduate students who have not taken college-level biology courses. We will examine biological systems such as DNA, proteins and membranes, first by giving a thorough description of their biological functions and then by analyzing their underlying physical principles.

Syllabus : Spring Fundamental concepts of crystalline solids, including crystal structure, band theory of electrons, and lattice vibration theory. Cross-list: ELEC Continuation of PHYS , including scattering of waves by crystals,transport theory, and magnetic phenomena. Mandel and E. Tentative Syllabus. Review of Quantum Mechanics: Hilbert space, operators, states, time evolution.

Two level systems - Pauli algebra, Bloch-sphere, magnetic resonance. Optical resonance for two level atoms. Atom-photon interaction in electric dipole approximation. Phenomenological damping - master equation and rate equations.

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Quantization of the electromagnetic field. Photon counting statistics -- Mandel's formula. Coherent states as quasi-classical states. Phase space methods - Quasiprobability distributions, P,Q, Wigner functions. Theory of partial coherence -- Glauber's correlation functions. Photon antibunching and resonance fluorescence. Jaynes-Cummings model -- Dressed states, collapse and revival.

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V Theory of dissipation in quantum mechanics. Derivation of the Linblad master equation in the Born-Markov approximation. Damped two-level atom and simple harmonic oscillators. Heisenberg formulation - Langevin equations. VII Theoretical methods for open quantum systems. Quantum trajectories -- Unraveling the master equation.

Lectures Notes in. Continuation Lect 3 PodCast-5 Sep. Laser spectroscopy as magnetic resonance Lecture 4. Two-level Atomic Response Lecture 5b. Lecture 6. PodCast-9 Sep. Lecture 7. Photon counting experiments and photon statistics. Lecture 9. Coherent states as quasiclassical states. PodCast Oct. Lectures 10 PodCast Oct. Lecture Optical coherence and photon statistics Lecture 13 PodCast Oct. Squeezed states - General properties Lecture Lecture 17 PodCast Nov. Tensor products, marginal density opertor, entanglement. Lecture 19 PodCast Nov.

Irreverisble bipartite system-reservoir interaction. Markov approximation - Lindblad Master Equation. Principles of general relativity — the equivalence principle; space-time effects of gravitation; gravitational redshifts; the curvature of spacetime; the geodesic equation.

Einstein's equations and their solutions — the Schwarzschild geometry for a spherical star; equation of orbit; experimental tests of general relativity; introduction to black hole physics. Introduction to quantum field theory QFT. Basic concepts of QFT — mathematical techniques; the path-integral formalism of quantum mechanics; canonical quantization, Green's functions; Feynman diagrams and perturbation theory.

Applications of QFT in particle physics and many-body condensed matter physics — quantum electrodynamics; the fractional quantum hall effect; mean-field theories of superfluids; renormalization group methods; the Landau-Ginzburg theory of critical phenomena. Introduction to solid state devices, with an emphasis on the modern microelectronics industry. Introduction to the physics of soft matter, such as colloids, foams, granular media, and liquid crystals.

Survey course in research topics at the frontiers of applied physics. The topics vary from semester to semester, and are chosen from the fields of materials physics, spintronics, photonics, organic devices, nanotechnology, superconducting devices, etc. Fundamentals of radiation physics, with a focus on clinical applications. Dosimetry — basic concepts and techniques; dose calculation methods; treatment planning. Radiobiology and radiotherapy; radiation safety.

Medical imaging and bio-sensing techniques, with special emphasis on the underlying physical principles. Photonics-based biosensors and their applications. Medical imaging techniques — instrumentation; applications for disease diagnosis and drug discovery; comparative analysis of different biomedical imaging and sesing techniques. Introduction to plasmonic waves in metallic materials, and metamaterials artificial materials with novel electromagnetic properties.

Physics of s urface plasmon polaritons — conductive properties of metals; plasmonic d ispersion relations; coupling light waves to plasmons. Two-semester research project, supervised by a faculty member, culminating in a thesis report and a seminar presentation. Click here for more information about the Final Year Project. Ten-week industrial placement attachment in an approved company or institution. Click here for more information. Twenty-two week industrial placement internship in an approved company or institution.

Ten-week attachment in an approved company or institution. Twenty-two week internship in an approved company or institution. Click here fore more information. Introduction to physics. Mechanics — vectors; kinematics; forces and torques; Newton's laws of motion; impulse and momentum; work and energy. Thermal physics. Electromagnetism — the electric field; the magnetic field; motion of charged particles; electrical circuits.

Prerequisite: Physics at A or H2 level, or equivalent. Introduction to physics, for students without A-level physics or equivalent. Fundamentals of physics, with an emphasis on practical applications in engineering, the biomedical sciences, and other fields.

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Students also learn how to read scientific material effectively, identify fundamental concepts, reason through scientific questions, and solve quantitative problems. Wave motion. Prerequisite: mathematics at the A or H2 level, or equivalent. Fundamentals of physics , with an emphasis on practical applications in engineering, the biomedical sciences, and other fields. Electricity and magnetism.

Modern physics. Introduction to the physical factors that govern the environment. Prerequisite: Physics at the O level, or equivalent. Introduction to the physical principles governing human locomotion and sports. Unrestricted Electives. Introduction to physics research, supervised by a faculty member. Suitable for undergradautes from year 2 onwards. Research topics are determined by the faculty supervisors. Methods for fabricating nano-scale thin-film, and their applications in modern materials technology.

Hands-on course in applying scientific knowledge to open-ended real life problems. Students are provided with the opportunity to freely explore open problems in multiple disciplines, and design projects to tackle those problems. The end-product of the investigation is a novel object or device, designed and created by the students.

The students must then present and answer questions about their project. Other Core Requirements for Physics Majors. Follow NTU sg. PH - Mechanics. Fundamental quantities of nature. Systems in equilibrium, in motion with constant acceleration and non-constant acceleration. Frames of reference and Galilean Relativity. PH - Optics, Vibrations and Waves. Oscillations — simple harmonic motion; relative phases; pendulums; damped and driven oscillations; phasor diagrams. PH - Electricity and Magnetism. Electrical circuits — voltage, current and resistance; oscillations in circuits; LC circuits and relative phases; complex descriptions of current, voltage, and impedance; LCR circuits and electrical resonance; high pass and low pass filters.

Electromagnetic Waves — properties of electromagnetic waves; the Poynting vector. Nuclear Physics and Radioactivity — radioactive decay; binding energy; activities and half-lives; fission and fusion; radiation doses. PH - Physics Laboratory Ia. PH - Physics Laboratory Ib. PH - Quantum Mechanics I. Solutions of time-independent Schrodinger equation — plane-wave solutions; step potential; barrier potential; quantum tunneling with examples in radioactive alpha-decay, ammonia molecule, tunnel diode, scanning tunneling microscope, etc.

One-electron atoms — central potentials; development of the Schrodinger equation in 3-dimensions; separation of variables; eigenvalues, quantum numbers and degeneracy; eigenfunctions; probability densities; orbital angular momentum; eigenvalue equations. Magnetic dipole moments and spin — orbital magnetic dipole moments; the Stern-Gerlach experiment and electron spin; spin-orbit interaction; total angular momentum. Electric dipole moment — polarization and displacement; multipole expansions.

## Quantum and classical optics–emerging links - IOPscience

Laplace's and Poisson's equations — uniqueness theorem; method of images; electrostatic energy. Maxwell's equations; relativistic invariance; the continuity equation. PH - Thermal Physics. Thermodynamic equilibrium; functions of state; equations of state; perfect gases and absolute zero; the zeroth law of thermodynamics. The first law of thermodynamics — work, heat, and internal energy; adiabatic, reversible and irreversible changes; heat engines, efficiency, and Carnot cycles.

Clausius' theorem and the Second law of thermodynamics. Fundamental equations of thermodynamics; phase changes and latent heat; enthalpy, Helmholtz free energy and Gibb's energy; Maxwell relations; the reciprocity theorem. The third law of thermodynamics. Kinetic theory — Maxwell distribution of velocities; pressure and effusion; mean free path; thermal conductivity and viscosity. Heat transport — conduction, radiation, and convection as transport mechanisms; heat flux and heat diffusion equation; steady-state and initial-value problems; sinusoidally varying surface temperatures.

PH - Analytical Mechanics. Newtonian Mechanics — m otion with non-constant acceleration; potential energy and conservative force; conservative forces in three dimensions; small oscillations; coupled oscillators; central forces; orbits and trajectories; scattering; collisions in center of mass coordinates. Rotating Systems — rotating coordinate systems; Coriolis forces and centrifugal forces; the Focault pendulum; rigid body rotation; inertia tensor, principal axes of inertia, and precession.

Intermediate experimental physics, including topics in electronics, nuclear physics, semiconductor physics, and spectroscopy. Intermediate experimental physics, including topics in optics, spectroscopy, X-ray physics, and statistical mechanics.

PH - Physical Optics. Properties of optical waves — refraction and dispersion; interference; the Michelson interferometer; Fraunhofer and Fresnel diffraction; the resolution limit; Fourier transformations; holography. Polarization; birefringence and wave plates; Fabry-Perot etalons; optical coatings; zone plates. PH - Introduction to Lasers. Postulats of quantum mechanics - quantum states and operators; wavefunctions; orthogonality and completeness; degeneracies; symmetries and conservation laws; the quantum-classical correspondence.

Angular momentum — operators, eigenvalues and eigenstates of angular momentum; parity and rotational invariance; the hydrogen atom; angular momentum quantum numbers.

## Quantum Optics and Fundamentals of Physics

Time-independent perturbation theory — non-degenerate eigenvalues; first and second order corrections; degenerate perturbation theory; the variational principle. Crystal symmetry — lattice, basis, unit cell of a crystal; Miller indices; lattice planes and spacings; the reciprocal lattice and Brillouin zones; Bragg and Laue diffraction; structure factor; atomic form factor; neutron and x-ray diffraction; powder and single crystal diffraction.

Sound propagation in solids — normal mode dispersion for linear atomic chains; acoustic and optical phonon modes; Born von Karman boundary conditions; density of states; lattice quantization and phonons; Einstein and Debye models of heat capacity. Electronic properties — free electron theory; density of states; the Fermi energy; Fermi surfaces; conductivity and heat capacity; the nearly-free electron model; band gaps; the Bloch theorem; the Kronig-Penny model. Distinctions between metals, semiconductors and insulators; aspects of condensed matter physics.

PH - Statistical Mechanics. Basic postulates of statistical mechanics — macrostates and microstates; distinguishable and indistinguishable particles; distribution functions. Temperature and entropy — state probabilities; the Boltzmann relation; the canonical ensemble; the partition function; Gibbs' entropy formula; the Third Law of thermodynamics; information theory; irreversible processes and the arrow of time. Density of states and heat capacity in black body radiation. Ideal classical gases — the Maxwell-Boltzmann distribution; rotational and vibrational heat.

Free electron gases — the Fermi energy and distribution function; Pauli paramagnetism; electronic contributions to heat capacity. Phonons — phonon contributions to heat capacity; the Debye approximation; the phonon gas; thermal conductivity of insulators. Phase transitions — the Weiss model of ferromagnetism; order-disorder transitions.