The courses listed below are pre-approved biological science courses offered at various Notre Dame study abroad locations.

More information about course groupings, academic requirements, available majors, and sample curriculum can be found in the Undergraduate Bulletin of Information 2013-2014.

## Perth, Australia

### PHYS 14140. Descriptive Astronomy

(3-0-3)

Taught as SCIE 1122 "Our Solar System" at host institution. This multidisciplinary unit provides a broad basic knowledge of the origin and evolution of the solar system and its planets, with emphasis on planet Earth. Lectures in this unit are in the form of modules entitled Planetary Systems; Habitable Planets; Third Rock from the Sun; Emergence of Life; and The Future of Our Planet. Students also participate in group projects and a field trip to the Gingin chalk fossil deposits, followed by an astronomy night.

### PHYS 44371. Biomeasurement

(3-0-3)

This unit comprises the following topics: sensing - the physics of the eye, vision, color, the ear, acoustics, ultrasound, sonar and neural processes; imaging - electron microscopy, confocal microscopy, X-ray diffraction, ultrasound, three-dimensional transforms, and MRI; transducers' instrumentation and the measurement of bio-electricity and bio-impedance, EEG, ECG, Fourier analysis, extracting, amplifying and filtering of a signal.

### PHYS 44602. Atoms, Nuclei, Particles, and Galaxies

(3-0-3)

This unit consists of 13 lectures on galaxies, 16 lectures on atomic and nuclear physics, 10 lectures on particle physics, and five 3-hour laboratory sessions. In addition to mastery of specific subject matter, students develop skills of critical analysis and problem solving via the assignment component of the unit, as well as quantitative skills via the laboratory component.

### PHYS 44602. Galaxies, Cosmology, and Space Science

(3-0-3)

Taught as PHYS3303 - 'Galaxies, Cosmology and Space Science' at a host institution. This is a core unit in the Astronomy and Astrophysics major in the Bachelor of Science (50110). It is also suitable for students in other majors who wish to gain an understanding of key elements of modern astronomy and astrophysics. Topics covered include modern cosmology, galaxy formation, dynamics and evolution, black holes, solar system and planetary physics and radiation mechanisms.

## London, England

### PHYS 34210. Physics I

(V-0-V)

The first semester of a two semester calculus-based introductory physics course intended primarily for students of the life sciences. The basic principles of mechanics, fluids, thermal physics, wave motion and sound are covered. Two semesters of an introductory calculus course are prerequisites. The usual related one hour lab will not be available. The one hour lab component is available in Puebla but not in London.

### PHYS 44880. Undergraduate Research

(V-0-V)

Research in collaboration with members of the faculty. Three to nine hours each week, arranged individually for each student. One to three credits.

## Oxford University, England

### PHYS 24454. Intermediate Mechanics

(3-0-3)

Newtonian mechanics of particles in one, two, and three dimensions; oscillations; non inertial reference frames; gravitation, central forces; systems of particles; kinetics and dynamics of rigid body motion; Lagrangians; Hamilton's equations.

### PHYS 24458. Mechanics II

(3-0-3)

Conservation laws for systems of particles; coupled oscillations; rotating coordinate systems; one-dimensional wave motion; gravitation; kinematics and dynamics of rigid body motion; Lagrange's equations.

### PHYS 34411. Junior Seminar

(1-0-1)

A discussion of current topics in physics by staff members.

### PHYS 34432. Optics

(V-0-V)

Principles and practical aspects of laser operation and applications in modern optics. Propagation of plane electromagnetic waves. Diffraction and interference of light. Gaussian beam propagation and optical resonators. Theory of laser oscillation. Gas, solid, semiconductor, and dye lasers. Detectors of optical radiation. Nonlinear optics. Applications in research and industry. Laboratory exercises include polarization, interference, Fourier optics, holography, gas, diode and turnable lasers, and harmonic generation. A course primarily intended for physics majors.

### PHYS 34458. Classical Mechanics

(3-0-3)

Conservation laws for systems of particles; coupled oscillations; rotating coordinate systems; one-dimensional wave motion; gravitation; kinematics and dynamics of rigid body motion; Lagrange's equations.

### PHYS 34461. Thermal Physics

(3-0-3)

Taught at a host institution. PHYC 30010 Thermodynamics and Statistical Physics at UCD; Themodynamics and Statistical Physics sees wide application across the sciences. This module derives its understanding from first principles and translates this to wide application for example in relation to fluids, solid-state, phase change, radiation and laser physics, boson and fermion statistics. Introduced and widely applied are tools such as concepts of exact and inexact differentials, Maxwell's relations and the Lagrange method of multipliers. When taught in Dublin Ireland: PHYC 30010 Thermodynamics and Statistical Physics at UCD; Themodynamics and Statistical Physics sees wide application across the sciences. This module derives its understanding from first principles and translates this to wide application for example in relation to fluids, solid-state, phase change, radiation and laser physics, boson and fermion statistics. Introduced and widely applied are tools such as concepts of exact and inexact differentials, Maxwell's relations and the Lagrange method of multipliers. When taught at Trinity: PI 4041 Post-Kantian Philosophy: Self-Reference and Self-Awareness at TCD; When we speak or think we cannot avoid making use of the personal pronoun. We say 'I think' 'I am in pain', 'I am hungry' or 'I was born in the last century'. In all these instances reference to a bearer of thought seem inevitable. Yet there are many who wish to convince us that what seems unavoidable, in everyday talk, is nothing other than a linguistic convention. The words ?I? and ?my? are mere adornments of speech. There is a ?necessity of syntax? which compels us to speak of a positional self, however as soon as we have a closer look we come to realize that the pronoun ?I? is not a place holder for anything in particular. Indeed, without much trouble we can replace the phrase ?I was thinking? with ?there was thinking going on?, and ?I am in pain with ?there is pain? since there is no self separable from the thought or the sensation of pain. Proof for this lies in the fact that we cannot perceive such a self but if at all only our objects of thoughts, feelings, sensations or impressions. This is why Hume already concluded that no introspection will ever yield a pure self. Against this view this course wishes to show why we need to hold fast to the claim that ?I? is a referring expression. There is something distinctive about the use of the first person pronoun. No description, not even one containing indexicals (other than the first person pronouns themselves) can be substituted for 'I'. We shall do this by focusing on the writings on Wittgenstein, Sartre, Kant and Husserl.

### PHYS 34471. Electricity and Magnetism

(3-0-3)

Taught at host institution. When taught at Trinity: PY3P02 Electromagnetic Interactions I at TCD; Part I: Electromagnetic Theory: Vector operators, Green's and Stokes' theorems; Coulomb's and Gauss' Laws; dipoles and polarization; electric susceptibility and displacement vector; polar dielectrics and Langevin analysis; potential and electric energy density; electrostatic boundary conditions and method of images; Biot-Savart and Ampere's Laws; magnetic dipole and magnetization; H vector; vector potential; magnetic energy density; magnetostatic boundary conditions; dia, para and ferro magnetism; Faraday's law of electromagnetic induction; magnetoelectric induction; Maxwell's equations; plane waves; Poynting vector. Part II: Quantum Optics & Lasers: Interaction of light with matter: black body radiation, the photoelectric effect, Einstein A and B coefficients. Light as photons. Coherence and fluctuations of real sources, correlation functions, photon statistics. Behavior of photons in beam splitters, interferometers and cavities. The Raman effect. Basic laser theory: absorption and gain cross-section, saturation of absorption and gain, cavity lifetime and longitudinal modes, transverse mode structure, Gaussian beams. Three and four level lasers and power output in continuous wave lasers. Transient laser behavior, relaxation oscillations, Q-switching, methods of Q-switching, mode-locking and methods of mode-locking. Specific laser systems: ruby and Nd-YAG/glass lasers, He-Ne laser, argon-ion laser, carbon-dioxide laser, excimer laser, dye laser and semiconductor diode laser.

### PHYS 34472. Electromagnetic Waves

(3-0-3)

Study of electromagnetic waves, physical optics, radiation from accelerating charges, and some topics from the special theory of relativity.

### PHYS 34473. Covariant Electromagnetism

(3-0-3)

Maxwells equations and the associated conservation laws for charge, energy and momentum. (Conservation of angular momentum is excluded.) Systems of units in electromagnetism. Electro-magnetic potentials and Lorentz gauge condition. Covariance of Maxwells equations under spatial rotations, duality, change of gauge and Lorentz transformations; Lorentz transformation properties of fields, potentials and currents. Gauge transformations in non-relativistic quantum mechanics; Aharonov-Bohm effect.

### PHYS 44453. Foundations of Quantum Mechanics

(3-0-3)

Taught as MAPH 30210 "Foundations of Quantum Mechanics" at host institution. This module starts with the formulation of Quantum Mechanics in its modern mathematical setting. Then several traditional models, including tunnelling and the Hydrogen atom are treated. Some time-dependent perturbation theory is introduced. The module ends with the notion of time evolution in Quantum Mechanics. Course outline: Mathematical Structure: Hilbert spaces, self-adjoint and unitary operators, spectral measures. Postulates of Quantum Mechanics: States, observables and measurements, the correspondence principle, the Heisenberg uncertainty principle. One-dimensional systems: The harmonic oscillator, creation and annihilation operators, potential barriers and wells, tunnelling. Angular momentum and the hydrogen atom. Approximations: Elements of time-independent perturbation theory, the WKB approximation. Time evolution in the Schrödinger and Heisenberg pictures. When taught in Dublin, Ireland the course PHYC 30030 Quantum Mechanics at UCD; Postulates of Quantum Mechanics. Operators, observables and eigenfunctions. Co-ordinate and momentum representations. Hermitian operators. Matrix methods. Uncertainty Principle. Ehrenfest's theorem. Harmonic Oscillator, Ladder operators. Angular momentum. Schrödinger theory of the hydrogen atom. Degeneracy. Fine-structure. Normal Zeeman effect. Pauli theory of electron spin. Stern-Gerlach experiment, Spin-orbit interaction. Total angular momentum. Clebsch-Gordan coefficients. Anomalous Zeeman effect. Time independent perturbation theory, charged harmonic oscillator, Stark effect. Variation method. When taught in Trinity: PY3P01 Quantum Mechanics at TCD; Mathematical foundations of quantum mechanics: description of quantum states and dynamical variables, eigenvalue equations, superposition principle, expectation values. Solution of Schrödinger equation for 1-dimensional systems: SHO using ladder operators, Kronig-Penney model. Angular momentum: calculation of spectrum using ladder operators, orbital angular momentum and parity, spin, addition of angular momenta. Solution of Schrödinger equation in 3 dimensions: the hydrogen spectrum, relativistic corrections and spin-orbit coupling. Time independent perturbation theory.

### PHYS 44454. Intro to Quantum Mechanics II

(3-0-3)

Taught at Oxford University Year Long Program.

### PHYS 54003. Mathematical Methods in Physics

(3-0-3)

A study of the methods of mathematical physics. Topics include linear vector spaces, matrices, group theory, complex variable theory, infinite series, special functions, and differential equations.

## Dublin, Ireland - UCD

### PHYS 24330. Experimental Physics

(3.5-0-3.5)

A brief review of geometrical optics. Wave motion. Superposition. Electromagnetic theory of light. Light propagation (reflection, Fermat's principle). Polarization. Interference. Amplitude splitting and wave front splitting interferometers. Fraunhofer diffraction. Special relativity. Introduction to topics in modern physics, such as applied optics, astrophysics and particle physics.

### PHYS 24435. Electromagnetism and Optics

(3-0-3)

Taught as PHYC 20010 "Electromagnetism and Optics" at host institution. This module is divided into two halves, the first covering Electromagnetism and the second Wave Optics. The Electromagnetism component explores the laws of classical Electricity and Magnetism (Conservation of Charge, the Lorentz force, Gauss's Law for the Electric Field, Gauss's Law for the Magnetic Field, Faraday's Law and the Ampere-Mawell Law), with emphasis on the application of the laws to a variety of problems. As the laws are developed the mathematical notation of vector calculus is introduced to express them in the form known as Maxwell's Equations. The Optics section describes the treatment of light from a wave perspective. Topics covered include the Electromagnetic Theory of Light, Propagation of Light (reflection and refraction, Huygen's and Fermat's Principles) , Polarization, Interference and Interferometers, and Fraunhoffer Diffraction. The experimental laboratory associated with this module includes a series of experiments to reinforce the concepts encountered in the lectures, and to develop the students' experimental, critical thinking and problem-solving skills. Students will also gain experience with instrumentation, computer interfacing, and data analysis utilizing the latest software packages.

### PHYS 24451. Math Methods in Physics

(3-0-3)

Taught as MAPH 30160 "Mathematics for Engineers VII - Differential Equations" at host institution. This course is designed to familiarize engineering students with ordinary and partial differential equations. Although general techniques applicable to arbitrary differential equations will be taught, the emphasis will be on solving the types of differential equations which appear in an engineering context; examples include electrical circuits, traffic flow problems, the wave/string equation, the heat equation, and Laplace's/Poisson's equation. These techniques include critical point classification and phase portraits, the method of characteristics, separation of variables, Fourier series/transforms and classification of 2nd-order linear partial differential equations.

### PHYS 24481. Exploring the Solar System

(3-0-3)

PHYC 20040 Exploring the Solar System at UCD; The physics of planetary and satellite interiors and atmospheres, along with orbital dynamics, are the major topics of this module, which begins with a treatment of the origin and formation of the solar system, including the process of planetesimal accretion. The phenomena of tides and the Roche tidal limit for planetary ring systems are explored within the context of Newtonian gravitation. Essentials of orbital dynamics for space-flight and solar-system exploration, including the Hohmann transfer orbit are developed. The orbital behavior of solar-system objects is examined and phenomena such as orbital resonances and Lagrangian points are discussed. The basic principles of radiation, thermodynamics and fluid dynamics are applied to gain an understanding of fundamental atmospheric phenomena in gas-giant and terrestrial planets. Applications, such as remote sensing of planetary atmospheres, are also introduced. Results from recent space probes are used to highlight the presentation throughout the module.

### PHYS 34461. Thermal Physics

(3-0-3)

Taught at a host institution. PHYC 30010 Thermodynamics and Statistical Physics at UCD; Themodynamics and Statistical Physics sees wide application across the sciences. This module derives its understanding from first principles and translates this to wide application for example in relation to fluids, solid-state, phase change, radiation and laser physics, boson and fermion statistics. Introduced and widely applied are tools such as concepts of exact and inexact differentials, Maxwell's relations and the Lagrange method of multipliers. When taught in Dublin Ireland: PHYC 30010 Thermodynamics and Statistical Physics at UCD; Themodynamics and Statistical Physics sees wide application across the sciences. This module derives its understanding from first principles and translates this to wide application for example in relation to fluids, solid-state, phase change, radiation and laser physics, boson and fermion statistics. Introduced and widely applied are tools such as concepts of exact and inexact differentials, Maxwell's relations and the Lagrange method of multipliers. When taught at Trinity: PI 4041 Post-Kantian Philosophy: Self-Reference and Self-Awareness at TCD; When we speak or think we cannot avoid making use of the personal pronoun. We say 'I think' 'I am in pain', 'I am hungry' or 'I was born in the last century'. In all these instances reference to a bearer of thought seem inevitable. Yet there are many who wish to convince us that what seems unavoidable, in everyday talk, is nothing other than a linguistic convention. The words ?I? and ?my? are mere adornments of speech. There is a ?necessity of syntax? which compels us to speak of a positional self, however as soon as we have a closer look we come to realize that the pronoun ?I? is not a place holder for anything in particular. Indeed, without much trouble we can replace the phrase ?I was thinking? with ?there was thinking going on?, and ?I am in pain with ?there is pain? since there is no self separable from the thought or the sensation of pain. Proof for this lies in the fact that we cannot perceive such a self but if at all only our objects of thoughts, feelings, sensations or impressions. This is why Hume already concluded that no introspection will ever yield a pure self. Against this view this course wishes to show why we need to hold fast to the claim that ?I? is a referring expression. There is something distinctive about the use of the first person pronoun. No description, not even one containing indexicals (other than the first person pronouns themselves) can be substituted for 'I'. We shall do this by focusing on the writings on Wittgenstein, Sartre, Kant and Husserl.

### PHYS 44453. Foundations of Quantum Mechanics

(3-0-3)

Taught as MAPH 30210 "Foundations of Quantum Mechanics" at host institution. This module starts with the formulation of Quantum Mechanics in its modern mathematical setting. Then several traditional models, including tunnelling and the Hydrogen atom are treated. Some time-dependent perturbation theory is introduced. The module ends with the notion of time evolution in Quantum Mechanics. Course outline: Mathematical Structure: Hilbert spaces, self-adjoint and unitary operators, spectral measures. Postulates of Quantum Mechanics: States, observables and measurements, the correspondence principle, the Heisenberg uncertainty principle. One-dimensional systems: The harmonic oscillator, creation and annihilation operators, potential barriers and wells, tunnelling. Angular momentum and the hydrogen atom. Approximations: Elements of time-independent perturbation theory, the WKB approximation. Time evolution in the Schrödinger and Heisenberg pictures. When taught in Dublin, Ireland the course PHYC 30030 Quantum Mechanics at UCD; Postulates of Quantum Mechanics. Operators, observables and eigenfunctions. Co-ordinate and momentum representations. Hermitian operators. Matrix methods. Uncertainty Principle. Ehrenfest's theorem. Harmonic Oscillator, Ladder operators. Angular momentum. Schrödinger theory of the hydrogen atom. Degeneracy. Fine-structure. Normal Zeeman effect. Pauli theory of electron spin. Stern-Gerlach experiment, Spin-orbit interaction. Total angular momentum. Clebsch-Gordan coefficients. Anomalous Zeeman effect. Time independent perturbation theory, charged harmonic oscillator, Stark effect. Variation method. When taught in Trinity: PY3P01 Quantum Mechanics at TCD; Mathematical foundations of quantum mechanics: description of quantum states and dynamical variables, eigenvalue equations, superposition principle, expectation values. Solution of Schrödinger equation for 1-dimensional systems: SHO using ladder operators, Kronig-Penney model. Angular momentum: calculation of spectrum using ladder operators, orbital angular momentum and parity, spin, addition of angular momenta. Solution of Schrödinger equation in 3 dimensions: the hydrogen spectrum, relativistic corrections and spin-orbit coupling. Time independent perturbation theory.

### PHYS 44470. Special Topics

(V-0-V)

Phase portraits, flows and evolution. Linear systems; Classification of linear systems, phase portraits of linear systems. Non-linear systems in the plane: Local and global behaviors, fixed points, linearization, stability of fixed points, limit points and limit cycles, Poincare-Bendixson theory. Non-linear systems in higher dimensions: Hyperbolic and non-hyperbolic fixed points, closed orbits, attracting sets and attractors. Chaotic orbits.

## Dublin, Ireland - Trinity College

### PHYS 34220. Physics II

(3-0-3)

"PY 1006 Electromagnetic Interactions at Trinity College; Electrostatics: electric charge, Coulomb's law, electric field, Gauss's law, electric potential energy, voltage, electric polarization, capacitance. Electricity: current, resistance, Ohm's law, electromotive force, power in electric circuits, Kirchoff's laws, RC circuits. Magnetism: magnetic pole, magnetostatic forces, magnetic fields, magnetic domains. Electromagnetism: force on a moving charge, magnetic torque, electric motors - DC and AC, field due to a moving charge, force between conductors. Electromagnetic induction: Faraday's law, Lenz's law." PY 2009 Current Electricity at Trinity College; Theory of metallic conduction, resistors, power dissipation, voltage dividers, voltage and current sources, Thevenin's theorem and Norton's theorem. Capacitors and R-C circuits. Review of magnetic field and magnetic force. The Hall effect, Ampere's Law and displacement current. Review of electromagnetic induction, mutual inductance and self-inductance. R-L circuits and L-R-C circuits. AC circuits, phasor diagrams, reactance, resonance, transformers and complex representation of reactance. R-C integration and differentiation, R-C low and high pass filters and active filters. Introduction to semiconductor devices: doping, p-n junction, rectification, and bipolar junction transistor.

### PHYS 34461. Thermal Physics

(3-0-3)

Taught at a host institution. PHYC 30010 Thermodynamics and Statistical Physics at UCD; Themodynamics and Statistical Physics sees wide application across the sciences. This module derives its understanding from first principles and translates this to wide application for example in relation to fluids, solid-state, phase change, radiation and laser physics, boson and fermion statistics. Introduced and widely applied are tools such as concepts of exact and inexact differentials, Maxwell's relations and the Lagrange method of multipliers. When taught in Dublin Ireland: PHYC 30010 Thermodynamics and Statistical Physics at UCD; Themodynamics and Statistical Physics sees wide application across the sciences. This module derives its understanding from first principles and translates this to wide application for example in relation to fluids, solid-state, phase change, radiation and laser physics, boson and fermion statistics. Introduced and widely applied are tools such as concepts of exact and inexact differentials, Maxwell's relations and the Lagrange method of multipliers.

### PHYS 34461. Topics in Modern Physics II

(3-0-3)

PY3P03 Condensed Matter I at TCD; Crystal systems, Bravais lattices, unit cell parameters, translational and rotational symmetry elements, point groups, space groups, Miller indices. The reciprocal lattice. X-ray and neutron scattering. Laue conditions, Bragg's Law. Diffraction patterns and their interpretation. Crystal field explained using the example of 3d electronic wave functions. Crystal defects. Points defects. Variation of the crystal field caused by point defects. Jahn-Teller effect. One-dimensional defects: dislocations. Energetics and thermodynamics of defects. Equilibrium density of point defects.

### PHYS 34471. Electricity and Magnetism

(3-0-3)

Taught at host institution. When taught at Trinity: PY3P02 Electromagnetic Interactions I at TCD; Part I: Electromagnetic Theory: Vector operators, Green's and Stokes' theorems; Coulomb's and Gauss' Laws; dipoles and polarization; electric susceptibility and displacement vector; polar dielectrics and Langevin analysis; potential and electric energy density; electrostatic boundary conditions and method of images; Biot-Savart and Ampere's Laws; magnetic dipole and magnetization; H vector; vector potential; magnetic energy density; magnetostatic boundary conditions; dia, para and ferro magnetism; Faraday's law of electromagnetic induction; magnetoelectric induction; Maxwell's equations; plane waves; Poynting vector. Part II: Quantum Optics & Lasers: Interaction of light with matter: black body radiation, the photoelectric effect, Einstein A and B coefficients. Light as photons. Coherence and fluctuations of real sources, correlation functions, photon statistics. Behavior of photons in beam splitters, interferometers and cavities. The Raman effect. Basic laser theory: absorption and gain cross-section, saturation of absorption and gain, cavity lifetime and longitudinal modes, transverse mode structure, Gaussian beams. Three and four level lasers and power output in continuous wave lasers. Transient laser behavior, relaxation oscillations, Q-switching, methods of Q-switching, mode-locking and methods of mode-locking. Specific laser systems: ruby and Nd-YAG/glass lasers, He-Ne laser, argon-ion laser, carbon-dioxide laser, excimer laser, dye laser and semiconductor diode laser.

### PHYS 34481. Modern Observational Technique

(3-0-3)

PY3A02 Astrophysics II at TCD; Spectroscopy across the full electromagnetic spectrum is the primary means for determining the properties and characteristics of astronomical objects. Some important parameters which characterize astronomical spectra, and which determine the choice of instrumentation are reviewed, with a brief outline of some examples. The underlying physics required for the interpretation of stellar spectra (for stellar classification) and for the diagnostics of low density plasmas is discussed and applied to some specific, topical examples.

### PHYS 44441. Modern Physics Laboratory I

(3-0-3)

PY3P07 Experimental Techniques at TCD; Scanning Probe Microscopes (Scanning Tunneling Microscopy, Scanning Force Microscope, Scanning Nearfield Optical Microscope); Sensors (tunneling current, force, optical, capacitance, piezoresistance); Motion (piezo electrics, stepper motors, etc.); Environments (UHV, Ambient, liquid, high temperature); Detectors for visible light: position sensitive detectors, photomultipliers, avalanche photodiodes, solid state junction detectors; Software interface (e.g. LabVIEW); Feedback electronics; Multiplexing; Optical tweezers; Cantilever Array devices; Functionalization strategies, description of current research.

### PHYS 44442. Modern Physics Laboratory II

(3-0-3)

PY3AP1 Practical in Astrophysics at TCD; course counts as PHYS 44442 and PHYS 34411 at ND.

### PHYS 44445. Stellar and Galactic Structure

(3-0-3)

Taught as PYA03 Stellar and Galactic Structure at TCD; Part I: Stellar Astrophysics: Stellar structure and evolution are regulated by the opposing effects of gravity and radiation pressure. Ultimately gravitational collapse will turn a star in a cold compact object, such as a white dwarf, a neutron star or possibly a black hole. Our understanding of the physics of the stars has produced remarkably good results in the last decades, allowing detailed predictions of observable quantities in the various stages of a stellar life. The course will briefly illustrate the underlying physics and discuss the comparison between theoretical predictions and observational results. Part II: Galaxies: From the Milky Way to Quasars: Gravitational forces determine the movements of the stars within a galaxy. Several aspects of this basic problem will be considered, such as space distribution of stars, stellar velocity distribution, high-velocity stars, rotation curve of stellar systems, integrals of motion, individual stellar orbits. The stars moving around in elliptical galaxies exhibit triaxial velocity ellipsoids, while the ordered motion in disk systems gives rise to spiral density patterns. The stellar movements indicate that large amounts of unseen mass may be associated with galaxies and with clusters of galaxies. Many details of stellar dynamics become evident in the close surroundings of our own Galaxy where a large body of observational data assists our understanding. Part II: Galaxies: From the Milky Way to Quasars: Gravitational forces determine the movements of the stars within a galaxy. Several aspects of this basic problem will be considered, such as space distribution of stars, stellar velocity distribution, high-velocity stars, rotation curve of stellar systems, integrals of motion, individual stellar orbits. The stars moving around in elliptical galaxies exhibit triaxial velocity ellipsoids, while the ordered motion in disk systems gives rise to spiral density patterns. The stellar movements indicate that large amounts of unseen mass may be associated with galaxies and with clusters of galaxies. Many details of stellar dynamics become evident in the close surroundings of our own Galaxy where a large body of observational data assists our understanding.

### PHYS 44453. Foundations of Quantum Mechanics

(3-0-3)

Taught as MAPH 30210 "Foundations of Quantum Mechanics" at host institution. This module starts with the formulation of Quantum Mechanics in its modern mathematical setting. Then several traditional models, including tunnelling and the Hydrogen atom are treated. Some time-dependent perturbation theory is introduced. The module ends with the notion of time evolution in Quantum Mechanics. Course outline: Mathematical Structure: Hilbert spaces, self-adjoint and unitary operators, spectral measures. Postulates of Quantum Mechanics: States, observables and measurements, the correspondence principle, the Heisenberg uncertainty principle. One-dimensional systems: The harmonic oscillator, creation and annihilation operators, potential barriers and wells, tunnelling. Angular momentum and the hydrogen atom. Approximations: Elements of time-independent perturbation theory, the WKB approximation. Time evolution in the Schrödinger and Heisenberg pictures. When taught in Dublin, Ireland the course PHYC 30030 Quantum Mechanics at UCD; Postulates of Quantum Mechanics. Operators, observables and eigenfunctions. Co-ordinate and momentum representations. Hermitian operators. Matrix methods. Uncertainty Principle. Ehrenfest's theorem. Harmonic Oscillator, Ladder operators. Angular momentum. Schrödinger theory of the hydrogen atom. Degeneracy. Fine-structure. Normal Zeeman effect. Pauli theory of electron spin. Stern-Gerlach experiment, Spin-orbit interaction. Total angular momentum. Clebsch-Gordan coefficients. Anomalous Zeeman effect. Time independent perturbation theory, charged harmonic oscillator, Stark effect. Variation method. When taught in Trinity: PY3P01 Quantum Mechanics at TCD; Mathematical foundations of quantum mechanics: description of quantum states and dynamical variables, eigenvalue equations, superposition principle, expectation values. Solution of Schrödinger equation for 1-dimensional systems: SHO using ladder operators, Kronig-Penney model. Angular momentum: calculation of spectrum using ladder operators, orbital angular momentum and parity, spin, addition of angular momenta. Solution of Schrödinger equation in 3 dimensions: the hydrogen spectrum, relativistic corrections and spin-orbit coupling. Time independent perturbation theory.

### PHYS 44454. Intro to Quantum Mechanics II

(3-0-3)

Taught at Oxford University Year Long Program.

### PHYS 54303. Quantum Optics

(3-0-3)

PY3P02 Electromagnetic Interactions at TCD;TCD Course counts as PHYS 34471 and PHYS 54303 at ND for 3 credits each for a total of 6 credits. Interaction of light with matter: black body radiation, the photoelectric effect, Einstein A and B coefficients. Light as photons. Coherence and fluctuations of real sources, correlation functions, photon statistics. Behavior of photons in beam splitters, interferometers and cavities. The Raman effect. Basic laser theory: absorption and gain cross-section, saturation of absorption and gain, cavity lifetime and longitudinal modes, transverse mode structure, Gaussian beams. Three and four level lasers and power output in continuous wave lasers. Transient laser behavior, relaxation oscillations, Q-switching, methods of Q-switching, mode-locking and methods of mode-locking. Specific laser systems: ruby and Nd-YAG/glass lasers, He-Ne laser, argon-ion laser, carbon-dioxide laser, excimer laser, dye laser and semiconductor diode laser.

### PHYS 54445. Astrophysics

(3-0-3)

PY3A01 Astrophysics I at TCD; Stellar structure and evolution are regulated by the opposing effects of gravity and radiation pressure. Ultimately gravitational collapse will turn a star in a cold compact object, such as a white dwarf, a neutron star or possibly a black hole. Our understanding of the physics of the stars has produced remarkably good results in the last decades, allowing detailed predictions of observable quantities in the various stages of a stellar life. The course will briefly illustrate the underlying physics and discuss the comparison between theoretical predictions and observational results.

## Puebla, Mexico

### PHYS 34210. Physics I

(V-0-V)

The first semester of a two semester calculus-based introductory physics course intended primarily for students of the life sciences. The basic principles of mechanics, fluids, thermal physics, wave motion and sound are covered. Two semesters of an introductory calculus course are prerequisites. The usual related one hour lab will not be available. The one hour lab component is available in Puebla but not in London.