* PHYS 0400a / ASTR 0400a, Expanding Ideas of Time and Space  Meg Urry

Discussions on astronomy, and the nature of time and space. Topics include the shape and contents of the universe, special and general relativity, dark and light matter, and dark energy. Observations and ideas fundamental to astronomers' current model of an expanding and accelerating four-dimensional universe. Enrollment limited to first-year students.   SC
TTh 2:35pm-3:50pm

* PHYS 0500a / APHY 0500a / ENAS 0500a, Science of Modern Technology and Public Policy  Daniel Prober

Examination of the science behind selected advances in modern technology and implications for public policy, with focus on the scientific and contextual basis of each advance. Topics are developed by the participants with the instructor and with guest lecturers, and may include nanotechnology, quantum computation and cryptography, renewable energy technologies, optical systems for communication and medical diagnostics, transistors, satellite imaging and global positioning systems, large-scale immunization, and DNA made to order. Enrollment limited to first-year students.   SC
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* PHYS 0700a, Nuclear Physics: The Good, The Bad, and the Misunderstood  Helen Caines

This course aims to introduce students to the basics of nuclear radiation and its uses. What exactly is radiation? How do we detect it? How come a little exposure can be good for us but too much deadly? Is nuclear energy a viable option? Is my cell phone dangerous? Should I get that dental x-ray? By the end of the course students are armed with necessary physics insights to answer the above questions and more. No prerequisites are required but completion of a high school physics course, or similar subject is preferred.  Enrollment limited to first-year students.   SC
TTh 9am-10:15am

* PHYS 0800b and PHYS 1000b / APHY 0800b and APHY 1000b / ENAS 0800b and ENAS 1000b / EPS 0800b / EVST 0080b and EVST 1000b, Energy, Environment, and Public Policy  Daniel Prober

The technology and use of energy. Impacts on the environment, climate, security, and economy. Application of scientific reasoning and quantitative analysis. Intended for non–science majors with strong backgrounds in math and science. Tours are be conducted of major examples of good energy design at Yale, including the Yale Power Plant and Kroon Hall. Students who take this course are not eligible to take APHY 100. Prerequisites: High school chemistry, physics, and Math. Calculus is not required. Enrollment limited to first-year students.  QR, SC
TTh 11:35am-12:50pm

* PHYS 1210La or b / MB&B 1210La or b, Introduction to Physics in Living Systems I: Observation and Analysis  Staff

MB&B/PHYS 1210L is a half-credit, half-semester lab course that introduces physics in the life sciences. All the labs in this series are inquiry-based labs that focus experimental design and practicing lab skills common to many biology and physics research labs. 1210L specifically introduces students to good data collection practices by iterative improvement of methodology and allows students to test quantitative and qualitative models. Students taking 1210L will also get practice giving short scientific talks. For students choosing to major in MB&B, this course may be used to fulfill the MB&B requirement for Practical Skills in physics. There are no prerequisites to this 0.5 credit class and is often taken during the same semester as another lab in the 1200 series. Priority is given to first-year students looking to fulfill medical school application requirements and students seeking to join research labs at Yale.  SC  0 Course cr
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* PHYS 1220La or b / MB&B 1220La or b, Introduction to Physics in Living Systems: Observation and Analysis II  Staff

MB&B/PHYS 1220L is a half-credit, half-semester lab course that introduces physics in the life sciences. All the labs in this series are inquiry-based labs that focus experimental design and practicing lab skills common to many biology and physics research labs. 1220L specifically introduces students to quantitative error propagation, device calibration, and data transformation. Students taking 1220L will also get practice developing scientific posters. For students choosing to major in MB&B, this course may be used to fulfill the MB&B requirement for Practical Skills in physics. There are no prerequisites to this 0.5 credit class and is often taken during the same semester as another lab in the 1200 series. Priority is given to first-year students looking to fulfill medical school application requirements and students seeking to join research labs at Yale.  0 Course cr
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* PHYS 1230La or b / MB&B 1230La or b / PHYS 123L, Introduction to Physics in Living Systems III: Mechanics  Staff

MB&B/PHYS 1230L is a half-credit, half-semester lab course that introduces physics in the life sciences. All the labs in this series are inquiry-based labs that focus experimental design and practicing lab skills common to many biology and physics research labs. 1230L specifically introduces students to the mechanics of living systems. Some topics include forces on the body, viscous environments, and transport/diffusion. Students taking 1230L will also get practice developing a short research proposal. For students choosing to major in MB&B, this course may be used to fulfill the MB&B requirement for Practical Skills in physics. There are no prerequisites to this 0.5 credit class and is often taken during the same semester as another lab in the 1200 series. Priority is given to first-year students looking to fulfill medical school application requirements and students seeking to join research labs at Yale.  0 Course cr
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* PHYS 1240La or b / MB&B 1240La or b, Introduction to Physics in Living Systems Laboratory IV: Electricity, Magnetism, and Radiation  Staff

MB&B/PHYS 1240L is a half-credit, half-semester lab course that introduces physics in the life sciences. All the labs in this series are inquiry-based labs that focus experimental design and practicing lab skills common to many biology and physics research labs. 1240L specifically introduces students to electricity, magnetism, and optics in life science research. Some topics include diffraction, microscopy, and electrophoresis. Students taking 1240L will also get practice giving short scientific talks. For students choosing to major in MB&B, this course may be used to fulfill the MB&B requirement for Practical Skills in physics. There are no prerequisites to this 0.5 credit class and is often taken during the same semester as another lab in the 1200 series. Priority is given to first-year students looking to fulfill medical school application requirements and students seeking to join research labs at Yale.  SC  0 Course cr
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PHYS 1510a / APHY 1510a / ENAS 1510a, Multivariable Calculus for Engineers  Claudia Cea

An introduction to multivariable calculus focusing on applications to engineering problems. Topics include vector-valued functions, vector analysis, partial differentiation, multiple integrals, vector calculus, and the theorems of Green, Stokes, and Gauss. Prerequisite: MATH 1150 or equivalent.  QR
MW 11:35am-12:50pm

PHYS 1650La and PHYS 1660Lb, General Physics Laboratory  Staff

A variety of individually self-contained experiments are roughly coordinated with the lectures in PHYS 1700, 1710, and 1800, 1810 and illustrate and develop physical principles covered in those lectures.  SC  0 Course cr per term
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* PHYS 1700a and PHYS 1710b, University Physics for the Life Sciences  Staff

An introduction to classical physics with special emphasis on applications drawn from the life sciences and medicine. Fall-term topics include vectors and kinematics, Newton's laws, momentum, energy, random walks, diffusion, fluid mechanics, mathematical modeling, and statistical mechanics. Spring-term topics include oscillations, waves, sound, electrostatics, circuits, Maxwell's equations, electromagnetic waves, gene circuits, and quantum mechanics. Essential mathematics are introduced and explained as needed. Completion of MATH 1120 or equivalent is prerequisite for PHYS 1700. Completion of PHYS 1700 is a prerequisite for PHYS 1710. MATH 1160 (or MATH 1150) is recommended prior to or concurrently with PHYS 1710.  QR, SC  0 Course cr per term
MW 11:35am-12:50pm

PHYS 1800a and PHYS 1810b, University Physics  Adriane Steinacker

A broad introduction to classical and modern physics for students who have some previous preparation in physics and mathematics. Fall-term topics include Newtonian mechanics, gravitation, waves, and thermodynamics. Spring-term topics include electromagnetism, special relativity, and quantum physics. Concurrently with MATH 1150 and 1200 or equivalents. See comparison of introductory sequences and laboratories in the YCPS. May not be taken for credit after PHYS 1700, 1710.  QR, SC
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PHYS 2000a and PHYS 2010b, Fundamentals of Physics  Staff

A thorough introduction to the principles and methods of physics for students who have good preparation in physics and mathematics. Emphasis on problem solving and quantitative reasoning. Fall-term topics include Newtonian mechanics, special relativity, gravitation, thermodynamics, and waves. Spring-term topics include electromagnetism, geometrical and physical optics, and elements of quantum mechanics. Prerequisite: MATH 1150 or equivalent. MATH 1200 and either MATH 2250 or MATH 2220, are generally taken concurrently. See comparison of introductory sequences and laboratories in the YCPS.  QR, SC
MW 11:35am-12:50pm

PHYS 2050La or b and PHYS 2060La or b, Modern Physical Measurement  Staff

A two-term sequence of experiments in classical and modern physics for students who plan to major in Physics. In the first term, the basic principles of mechanics, electricity, and magnetism are illustrated in experiments designed to make use of computer data handling and teach error analysis. In the second term, students plan and carry out experiments illustrating aspects of wave and quantum phenomena and of atomic, solid state, and nuclear physics using modern instrumentation. May be begun in either term.  SC  0 Course cr per term
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* PHYS 2600a and PHYS 2610b, Intensive Introductory Physics  Staff

An introduction to major branches of physics—classical and relativistic mechanics; gravitation; electricity and magnetism; and quantum physics,information, and computation—at a sophisticated level. For students majoring in the physical sciences, mathematics, and philosophy whose high school training included both mechanics and electricity and magnetism at the typical college/AP level and have excellent training in, and a flair for, mathematical methods and quantitative analysis. Concurrently with MATH 1200, ENAS 1510, PHYS 1510, or PHYS 4000, or equivalent. Students considering an alternative MATH course should check with the DUS in Physics.  QR, SC
MW 11:35am-12:50pm

* PHYS 2710a and PHYS 2720b, Independent Research in Physics  Reina Maruyama

Each student works on an independent project under the supervision of a member of the faculty or research staff. Students participate in a series of seminar meetings in which they present a talk on their project or research related to it. A written report is also required. For students with a strong background in physics coursework. This course may be taken multiple times for pass/fail credit. Suggested for first years and sophomores.
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PHYS 3440a, Quantum and Nanoscale Physics  Charles Brown

An introduction to cutting-edge developments in physics involving quantum information and/or nanotechnology. Background concepts in quantum mechanics, electromagnetism, and optics are introduced as necessary. Prerequisite: PHYS 170, 171, or 180, 181, or 200, 201, or 260, 261, or permission of instructor. PHYS 301 or other advanced mathematics course recommended.  QR, SC
TTh 9am-10:15am

PHYS 3450b, Introduction to Quantum Information Processing and Communication  Aleksander Kubica

This course is intended for undergraduate physics, chemistry, engineering, computer science, statistics and data science, and mathematics majors seeking an introduction to quantum information science. There is now a second quantum revolution underway and a world-wide race to build powerful new types of computers based on quantum principles, and to develop new techniques for encrypted communication whose security is guaranteed by the laws of quantum mechanics. The approach of this course to these topics will strip away much of the traditional physics details to focus on the information content of quantum systems, the nature of measurement, and why the true randomness of certain measurement results can be a feature rather than a bug. We learn what it means for a quantum bit (‘qubit’) to be simultaneously 0 and 1 (in some sense). We learn about quantum entanglement and the associated ‘spooky action at a distance’ that convinced Einstein that the quantum theory must be wrong. Ironically, this bizarre effect is now used on a daily basis to prove that quantum mechanics is indeed correct and used as a routine engineering test to make sure that quantum computers are working properly and are truly quantum. Specific topics include: the mathematical representation of quantum states as complex vectors, the superposition principle, entanglement and Bell inequalities, quantum gates and algorithms for quantum computers, quantum error correction, dense coding, teleportation, and secure quantum communication. Students learn to do problem sets based on programming and operating publicly-accessible cloud-based quantum computers. See for example: https://www.ibm.com/quantum-computing/. Familiarity with complex numbers and the basics of linear algebra (matrices, determinants, eigenvectors and eigenvalues) is assumed. Prior exposure to basic probability and statistics. as well as a course in quantum mechanics are useful but not required.    SC
MW 9am-10:15am

PHYS 3530a / BENG 3500a, Introduction to Biomechanics  Jay Humphrey

An introduction to the biomechanics used in biosolid mechanics, biofluid mechanics, biothermomechanics, and biochemomechanics. Diverse aspects of biomedical engineering, from basic mechanobiology to the design of novel biomaterials, medical devices, and surgical interventions. Prerequisites: PHYS 1800, PHYS 1810, MATH 1150, and ENAS 1940.  QR  0 Course cr
TTh 9am-10:15am

* PHYS 3780b, Introduction to Scientific Computing & Data Science  Christopher Lynn

This course introduces students to essential computational and data analysis methods and tools and their problem-solving applications. These are skills and knowledge essential for beginning research in the sciences, and are not typically taught in an introductory physics curriculum. The goal here is not completeness across any of these areas, but instead the introduction of the most important and useful skills, concepts, methods, techniques, tools and relevant knowledge for getting started in research in physics. Key learning goals include basic programming in Python, data analysis, modeling, simulations and machine learning, and their applications to problems in physics and beyond.  Prerequisites: Introductory physics and familiarity with single variable calculus (basic integration, differentiation, Taylor series, etc). Previous experience in Python programming is not required. Contact instructor if you are unsure about your preparation.  SC
F 1:30pm-3:25pm

PHYS 3930a / APHY 3930a, Einstein and the Birth of Modern Physics  A Douglas Stone

The first twenty-five years of the 20th century represent a turning point in human civilization as for the first time mankind achieved a systematic and predictive understanding of the atomic level constituents of matter and energy, and the mathematical laws which describe the interaction of these constituents. In addition, the General Theory of Relativity opened up for the first time a quantitative study of cosmology, of the history of the universe as a whole. Albert Einstein was at the center of these breakthroughs, and also became an iconic figure beyond physics, representing scientist genius engaged in pure research into the fundamental laws of nature. This course addresses the nature of the transition to modern physics, underpinned by quantum and relativity theory, through study of Einstein’s science, biography, and historical context. It also presents the basic concepts in electromagnetic theory, thermodynamics and statistical mechanics, special theory of relativity, and quantum mechanics which were central to this revolutionary epoch in science. Prerequisites: Two terms of PHYS 170, 171, or PHYS 180, 181, or PHYS 200, 201, or PHYS 260, 261, or one term of any of these course with permission of instructor.   QR, SC
TTh 1:05pm-2:20pm

PHYS 3950a / ASTR 2550a, Research Methods in Astrophysics  Malena Rice

An introduction to research methods in astronomy and astrophysics. The acquisition and analysis of astrophysical data, including the design and use of ground- and space-based telescopes, computational manipulation of digitized images and spectra, and confrontation of data with theoretical models. Examples taken from current research at Yale and elsewhere. Use of the Python programming language. Prerequisite: background in high school calculus and physics. No previous programming experience required.  QR, SC  RP
MWF 10:30am-11:20am

* PHYS 3960b, The Impact of the Atom  Steve Lamoreaux

Born in secrecy, the power of the atom was revealed to the world over Hiroshima in 1945. Since then, the atom has touched every facet of our lives. This seminar explores issues on how the atom has impacted the world using a multidisciplinary approach. These topics may include the impact of the atom on history,  infrastructure, budget, arts and culture, peace and activism, healthcare, energy and climate change, policy, national security, international relations, science, and the future. Weekly assignments are supplemented with movie screenings and guest speakers.  Prerequisites: One term of PHYS 1700, 1710, or PHYS 1800, 1810, or PHYS 2000, 2010, or PHYS 2600, 2610, or permission of instructor.  SO
T 4pm-5:55pm

PHYS 4000a, Introduction to Mathematical Methods of Physics  Simon Mochrie

An introduction to the mathematical tools and concepts needed to study and model physical phenomena. Topics include linear algebra, differential equations, and dynamical systems. Designed to give accelerated access to 4000-level courses. Recommended to be taken concurrently with PHYS 4010 or 4100. Prerequisites: PHYS 1700, 1710, or 1800, 1810, or 2000, 2010, or 2600, 2610, or permission of instructor.  QR
TTh 11:35am-12:50pm

PHYS 4010a and PHYS 4020b, Advanced Classical Physics from Newton to Einstein  Staff

Advanced physics as the field developed from the time of Newton to the age of Einstein. Topics include mechanics, electricity and magnetism, statistical physics, and thermodynamics. The development of classical physics into a "mature" scientific discipline, an idea that was subsequently shaken to the core by the revolutionary discoveries of quantum physics and relativity. Prerequisite: PHYS 1700, 1710, or 1800, 1810, or 2000, 2010, or 2600, 2610. Concurrently with PHYS 4000 or other advanced mathematics course.  QR, SC
MW 9am-10:15am

PHYS 4100a, Classical Mechanics  Konrad Lehnert

An advanced treatment of mechanics, with a focus on the methods of Lagrange and Hamilton. Lectures and problems address the mechanics of particles, systems of particles, and rigid bodies, as well as free and forced oscillations. Introduction to chaos and special relativity. Prerequisite: PHYS 1700, 1710, or 1800, 1810, or 2000, 2010, or 2600, 2610. Concurrently with PHYS 4000 or other advanced mathematics course.  QR, SC
MW 9am-10:15am

PHYS 4120b, Relativity  Walter Goldberger

This course covers special relativity and an introduction to general relativity. A thorough treatment of special relativity, stressing equally conceptual understanding and certain formal aspects. Introduction to general relativity covers curved spaces, Einstein's equations, and some of their solutions. Prerequisite: PHYS 4010 or PHYS 4100.  QR, SC
TTh 2:35pm-3:50pm

PHYS 4300b, Electromagnetic Fields and Optics  Eduardo Higino da Silva Neto

Electrostatics, magnetic fields of steady currents, electromagnetic waves, and relativistic dynamics. Provides a working knowledge of electrodynamics. Prerequisites: PHYS 4000 and 4100 or equivalents.  QR, SC
TTh 9am-10:15am

PHYS 4390a / APHY 4390a, Basic Quantum Mechanics  John Sous

The basic concepts and techniques of quantum mechanics essential for solid-state physics and quantum electronics. Topics include the Schrödinger treatment of the harmonic oscillator, atoms and molecules and tunneling, matrix methods, and perturbation theory. Prerequisites: PHYS 1810 or 2010, PHYS 3010, or equivalents, or permission of instructor.  QR, SC
MW 2:35pm-3:50pm

PHYS 4400a, Quantum Mechanics and Natural Phenomena I  Witold Skiba

The first term of a two-term sequence covering principles of quantum mechanics with examples of applications to atomic physics. The solution of bound-state eigenvalue problems, free scattering states, barrier penetration, the hydrogen-atom problem, perturbation theory, transition amplitudes, scattering, and approximation techniques. Prerequisite: PHYS 4100 or 4010.  QR, SC
MW 11:35am-12:50pm

PHYS 4410b, Quantum Mechanics and Natural Phenomena II  Witold Skiba

Continuation of PHYS 4400. Prerequisite: PHYS 4400 and either PHYS 4300 or permission of the instructor.  QR, SC
MW 11:35am-12:50pm

PHYS 4420b, Introduction to Nuclear and Elementary Particle Physics  Laura Havener

Fundamental concepts in nuclear and particle physics, including the discovery of radioactivity, the Dirac equation, antimatter, Feynman diagrams, hadron resonances, quarks and gluons, fundamental symmetries, the weak interaction, beta decay, quantum chromodynamics, neutrino oscillation, unification, and particle theories for dark matter. Prerequisite: two term courses in quantum mechanics.  QR, SC
TTh 2:35pm-3:50pm

PHYS 4441a / AMTH 4441a / APHY 4410a / MENG 4441a, Nonlinear Dynamics  Bauyrzhan Primkulov

This course introduces nonlinear dynamics and chaos in dissipative systems, tailored broadly for undergraduate students in science and engineering. It focuses on simple dynamical models, the mathematical principles underlying their behaviors, their connection to natural phenomena, and techniques for data analysis and interpretation. Key topics include forced and parametric oscillators, phase space analysis, periodic, quasiperiodic, and aperiodic flows, sensitivity to initial conditions, and strange attractors such as the Lorenz attractor. The course also explores phenomena like period doubling, intermittency, and quasiperiodicity, emphasizing nonlinear processes describable by a limited number of time-evolving variables. ENAS 1510 (Multivariable Calculus or equivalent), ENAS 1940 (Differential Equations or equivalent)  SC
TTh 11:35am-12:50pm

* PHYS 4450La or b, Advanced Physics Laboratory  Staff

Laboratory experiments with some discussion of theory and techniques. An advanced course focusing on modern experimental methods and concepts in atomic, optical, nuclear, and condensed matter physics. Intended to prepare students for independent research. For majors in the physical sciences. After or concurrently with PHYS 4390 or 4400, or with permission of instructor. PHYS 2060L  WR, SC  0 Course cr
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PHYS 4480a / APHY 4480a, Solid State Physics I  Yu He

The first term of a two-term sequence covering the principles underlying the electrical, thermal, magnetic, and optical properties of solids, including crystal structure, phonons, energy bands, semiconductors, Fermi surfaces, magnetic resonances, phase transitions, dielectrics, magnetic materials, and superconductors. Prerequisites: APHY 3220, 4390, PHYS 4200.  QR, SC
MW 11:35am-12:50pm

PHYS 4490b / APHY 4490b, Solid State Physics II  Vidvuds Ozolins

The second term of the sequence described under APHY 448.  QR, SC
MW 11:35am-12:50pm

* PHYS 4500a / APHY 4200a, Thermodynamics and Statistical Mechanics  Steven Girvin

This course is subdivided into two topics. We study thermodynamics from a purely macroscopic point of view and then we devote time to the study of statistical mechanics, the microscopic foundation of thermodynamics. Prerequisites: PHYS 4000, 4100, and 4400 or permission of instructor.  QR, SC
MW 1:05pm-2:20pm

PHYS 4580a / APHY 4580a, Principles of Optics with Applications  Hui Cao

Introduction to the principles of optics and electromagnetic wave phenomena with applications to microscopy, optical fibers, laser spectroscopy, and nanostructure physics. Topics include propagation of light, reflection and refraction, guiding light, polarization, interference, diffraction, scattering, Fourier optics, and optical coherence. Prerequisite: PHYS 4300.  QR, SC
TTh 11:35am-12:50pm

* PHYS 4710a and PHYS 4720b, Independent Projects in Physics  Reina Maruyama

Each student works on an independent project under the supervision of a member of the faculty or research staff. Students participate in a series of seminar meetings in which they present a talk on their project or research related to it. A written report is also required. Registration is limited to junior and senior physics majors. This course may be taken up to four times for a letter grade.   
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