Physics

PHYS UN1001 PHYSICS FOR POETS. 3.00 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: high school algebra.
Prerequisites: high school algebra. This course does not fulfill the physics requirement for admission to medical school. No previous background in physics is expected. An introduction to physics taught through the exploration of the scientific method, and the application of physical principles to a wide range of topics from quantum mechanics to cosmology

PHYS UN1018 WEAPONS OF MASS DESTRUCTION. 3.00 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: high school science and math.
Prerequisites: high school science and math. A review of the history and environmental consequences of nuclear, chemical, and biological weapons of mass destruction (WMD); of how these weapons work, what they cost, how they have spread, how they might be used, how they are currently controlled by international treaties and domestic legislation, and what issues of policy and technology arise in current debates on WMD. What aspects of the manufacture of WMD are easily addressed, and what aspects are technically challenging? It may be expected that current events/headlines will be discussed in class

PHYS UN1111 ORIGINS AND MEANING. 3.00 points.

This course is a one-semester journey across cosmological history, from the beginning of time to something akin to its end. We will explore the origin of inanimate physical structures (the cosmos as a whole, as well as that of galaxies, stars, planets, particles, atoms and complex molecules), the origin of life (replicating molecules, the first cells, as well as more complex life forms), the origin of mind (self-reflective conscious awareness) and the origin of culture (language, myth, religion, art, and science). We will then consider what science in particular tells us about the very far future, where we will encounter the likely demise of all complex matter, all life and all consciousness. In the face of such disintegration we will examine the nature of value and purpose. We will recognize that the deepest understanding of reality emerges from blending all of the accounts we discuss—from the reductionist to the humanist to the cosmological—and only through such amalgamation can we fully grasp the long-standing human search for meaning

PHYS UN1201 GENERAL PHYSICS I. 3.00 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: some basic background in calculus or be concurrently taking MATH UN1101 Calculus I.,The accompanying laboratory is PHYS UN1291-UN1292
Prerequisites: some basic background in calculus or be concurrently taking MATH UN1101 Calculus I. The accompanying laboratory is PHYS UN1291-UN1292 The course will use elementary concepts from calculus. The accompanying laboratory is PHYS UN1291 - UN1292. Basic introduction to the study of mechanics, fluids, thermodynamics, electricity, magnetism, optics, special relativity, quantum mechanics, atomic physics, and nuclear physics

PHYS UN1202 GENERAL PHYSICS II. 3.00 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: This course will use elementary concepts from calculus. Students should therefore have had some high school calculus, or be concurrently enrolled in MATH UN1101. Taken with accompanying lab PHYS UN1291- PHYS UN1292, the sequence PHYS UN1201- PHYS UN1202 satisfies requirements for medical school.
Prerequisites: This course will use elementary concepts from calculus. Students should therefore have had some high school calculus, or be concurrently enrolled in MATH UN1101. Taken with accompanying lab PHYS UN1291- PHYS UN1292, the sequence PHYS UN1201- PHYS UN1202 satisfies requirements for medical school. Electricity, magnetism, optics, and modern physics

PHYS UN1203 GENERAL PHYSICS I - REC. 0.00 points.

PHYS UN1204 GENERAL PHYSICS II - REC. 0.00 points.

PHYS UN1291 GENERAL PHYSICS I LAB. 1.00 point.

Same course as PHYS W1291x, but given off-sequence.

Corequisites: PHYS UN1201
Corequisites: PHYS UN1201 This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture

PHYS UN1292 GENERAL PHYSICS II LABORATORY. 1.00 point.

Corequisites: PHYS UN1201,PHYS UN1202
Corequisites: PHYS UN1201,PHYS UN1202 This course is the laboratory for the corequisite lecture course (PHYS UN1201 - PHYS UN1202) and can be taken only during the same term as the corresponding lecture

PHYS UN1401 INTRO TO MECHANICS ＆ THERMO. 3.00 points.

CC/GS: Partial Fulfillment of Science Requirement

Corequisites: MATH UN1101
Corequisites: MATH UN1101 Fundamental laws of mechanics, kinematics and dynamics, work and energy, rotational dynamics, oscillations, gravitation, fluids, temperature and heat, gas laws, the first and second laws of thermodynamics. Corequisite: MATH UN1101 or the equivalent

PHYS UN1402 INTRO ELEC/MAGNETSM ＆ OPTCS. 3.00 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: PHYS UN1401
Corequisites: MATH UN1102
Prerequisites: PHYS W1401. Corequisites: MATH V1102 or the equivalent. Electric fields, direct currents, magnetic fields, alternating currents, electromagnetic waves, polarization, geometrical optics, interference, and diffraction

PHYS UN1403 INTRO-CLASSCL ＆ QUANTUM WAVES. 3.00 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: PHYS UN1402 PHYS W1402.
Corequisites: MATH V1201 or the equivalent.
Prerequisites: PHYS UN1402 PHYS W1402. Corequisites: MATH V1201 or the equivalent. Classical waves and the wave equation, Fourier series and integrals, normal modes, wave-particle duality, the uncertainty principle, basic principles of quantum mechanics, energy levels, reflection and transmission coefficients, applications to atomic physics

PHYS UN1404 INTRO TO MECH ＆ THERMO - REC. 0.00 points.

PHYS UN1405 INTRO ELEC/MAGNETSM/OPT-REC. 0.00 points.

PHYS UN1493 INTRO TO EXPERIMENTAL PHYS-LAB. 3.00 points.

PHYS UN1494 INTRO TO EXPERIMENTAL PHYS-LAB. 3.00 points.

Prerequisites: PHYS UN1401 and PHYS UN1402
Prerequisites: PHYS W1401 and W1402. Laboratory work associated with the two prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic physics, and nuclear physics. Note: Students cannot receive credit for both PHYS W1493 and W1494

PHYS UN1601 PHYSICS I:MECHANICS/RELATIVITY. 3.50 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: Corequisite: MATH UN1102 Calculus II or equivalent.
Prerequisites: Corequisite: MATH UN1102 Calculus II or equivalent. Fundamental laws of mechanics, kinematics and dynamics, work and energy, rotational dynamics, oscillations, gravitation, fluids, introduction to special relativity and relativistic kinematics. The course is preparatory for advanced work in physics and related fields

PHYS UN1602 PHYSICS II: THERMO, ELEC ＆ MAG. 3.50 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: PHYS UN1601 Corequisite: MATH UN1201 or equivalent.
Prerequisites: PHYS UN1601 Corequisite: MATH UN1201 or equivalent. Temperature and heat, gas laws, the first and second laws of thermodynamics, kinetic theory of gases, electric fields, direct currents, magnetic fields, alternating currents, electromagnetic waves. The course is preparatory for advanced work in physics and related fields

PHYS UN1603 PHYSICS I:MECHANICS/RELATIVITY-REC. 0.00 points.

PHYS UN1604 PHYSICS II:THERMO,ELEC/MAG-REC. 0.00 points.

PHYS UN2001 SPECIAL RELATIVITY. 3.00 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: a working knowledge of high school algebra, trigonometry, and physics. Some familiarity with calculus is useful but not essential.

This course is a comprehensive, one-semester introduction to the essential ideas and mathematical structures underlying Einstein’s Special Theory of Relativity. Among the topics covered will be: the relativity of simultaneity, time dilation, Lorentz contraction, velocity combination laws, time dilation over large distances, the Lorentz transformation, spacetime diagrams, the basic (seeming) paradoxes of special relativity, relativistic equations of motion and E = mc2.

PHYS UN2601 PHYSICS III:CLASS/QUANTUM WAVE. 3.50 points.

Prerequisites: PHYS UN1402 or PHYS UN1602 Corequisite: MATH UN1202 or equivalent.
Prerequisites: PHYS UN1402 or PHYS UN1602 Corequisite: MATH UN1202 or equivalent. Classical waves and the wave equation, geometrical optics, interference and diffraction, Fourier series and integrals, normal modes, wave-particle duality, the uncertainty principle, basic principles of quantum mechanics, energy levels, reflection and transmission coefficients, the harmonic oscillator. The course is preparatory for advanced work in physics and related fields

PHYS UN2603 Physics III: Class/Quantum Wave - Rec. 0.00 points.

PHYS UN2699 Experiments in Classical and Modern Physics. 3 points.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: (PHYS UN1601 or PHYS UN1401) and (PHYS UN1602 or PHYS UN1402) and PHYS UN2601 PHYS W1601 (or W1401), W1602 (or W1402), and W2601.

Laboratory work associated with the three prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic physics, and nuclear physics.

PHYS UN2801 ACCELERATED PHYSICS I. 4.50 points.

Prerequisites: Advanced Placement in physics and mathematics, or the equivalent, and the instructor's permission. (A special placement meeting is held during Orientation.)
Prerequisites: Advanced Placement in physics and mathematics, or the equivalent, and the instructor's permission. (A special placement meeting is held during Orientation.) This accelerated two-semester sequence covers the subject matter of PHYS UN1601, PHYS UN1602 and PHYS UN2601, and is intended for those students who have an exceptionally strong background in both physics and mathematics. The course is preparatory for advanced work in physics and related fields. There is no accompanying laboratory; however, students are encouraged to take the intermediate laboratory, PHYS UN3081, in the following year

PHYS UN2802 ACCELERATED PHYSICS II. 4.50 points.

Prerequisites: PHYS UN2801
Prerequisites: PHYS UN2801 This accelerated two-semester sequence covers the subject matter of PHYS UN1601, PHYS UN1602 and PHYS UN2601, and is intended for those students who have an exceptionally strong background in both physics and mathematics. The course is preparatory for advanced work in physics and related fields. There is no accompanying laboratory; however, students are encouraged to take the intermediate laboratory, PHYS UN3081, in the following year

PHYS UN2803 ACCELERATED PHYSICS I-REC. 0.00 points.

PHYS UN2804 ACCELERATED PHYSICS II-REC. 0.00 points.

Required discussion section for PHYS UN2802 Accelerated Physics II

PHYS UN3002 From Quarks To the Cosmos: Applications of Modern Physics. 3.5 points.

Prerequisites: PHYS UN2601 or PHYS UN2802

This course reinforces basic ideas of modern physics through applications to nuclear physics, high energy physics, astrophysics and cosmology. The ongoing Columbia research programs in these fields are used as practical examples. The course is preparatory for advanced work in physics and related fields.

PHYS UN3003 MECHANICS. 3.00 points.

Prerequisites: general physics, and differential and integral calculus.
Prerequisites: general physics, and differential and integral calculus. Newtonian mechanics, oscillations and resonance, conservative forces and potential energy, central forces, non-inertial frames of reference, rigid body motion, an introduction to Lagranges formulation of mechanics, coupled oscillators, and normal modes

PHYS UN3007 ELECTRICITY-MAGNETISM. 3.00 points.

Prerequisites: general physics, and differential and integral calculus.
Prerequisites: general physics, and differential and integral calculus. Electrostatics and magnetostatics, Laplace's equation and boundary-value problems, multipole expansions, dielectric and magnetic materials, Faraday's law, AC circuits, Maxwell's equations, Lorentz covariance, and special relativity

PHYS UN3008 ELECTROMAGNETIC WAVES ＆ OPTICS. 3.00 points.

Prerequisites: PHYS UN3008
Prerequisites: PHYS UN3008 Maxwells equations and electromagnetic potentials, the wave equation, propagation of plane waves, reflection and refraction, geometrical optics, transmission lines, wave guides, resonant cavities, radiation, interference of waves, and diffraction

PHYS UN3072 SEM IN CURRENT RES. PROBLEMS. 2.00 points.

A detailed study of a selected field of active research in physics. The motivation, techniques, and results obtained to the present, as well as the difficulties and unsolved problems. For Physics majors only. Priority given to seniors; juniors by permission of the instructor

PHYS UN3081 INTERMEDIATE LABORATORY WORK. 2.00 points.

May be repeated for credit by performing different experiments. The laboratory has available fifteen individual experiments, of which two are required per 2 points.

Prerequisites: PHYS UN2601 or PHYS UN2802 Primarily for junior and senior physics majors; other majors must obtain the instructor's permission.
Prerequisites: PHYS UN2601 or PHYS UN2802 Primarily for junior and senior physics majors; other majors must obtain the instructors permission. Each experiment is chosen by the student in consultation with the instructor. Each section meets one afternoon per week, with registration in each section limited by the laboratory capacity. Experiments (classical and modern) cover topics in electricity, magnetism, optics, atomic physics, and nuclear physics

PHYS UN3083 ELECTRONICS LABORATORY. 3.00 points.

Enrollment limited to the capacity of the laboratory.

Prerequisites: PHYS UN3003 or PHYS UN3007 May be taken before or concurrently with this course.
Prerequisites: PHYS UN3003 or PHYS UN3007 May be taken before or concurrently with this course. A sequence of experiments in solid-state electronics, with introductory lectures

PHYS UN3084 Quantum Simulation and Computing Lab. 3.00 points.

The “Quantum Simulation and Computing Lab” will give students hands-on experience in quantum optics, quantum simulation and quantum computing. The course combines lectures, tutorials, and two lab sections. In one lab section, students will do experiments with entangled photons. In the second lab section, students will program quantum computers and run algorithms on them using the IBM Qiskit platform. The course starts with a recap of linear algebra and quantum mechanics, followed by an introduction to quantum optics and quantum information. Two-level systems, Bloch sphere, quantum gates, and elementary quantum algorithms will be discussed. Quantum teleportation and quantum key distribution will be introduced as applications of entanglement. The lecture content will be directly applied in experiments with entangled photons. In the following, state-of-the-art quantum algorithms will be discussed, related to cutting-edge research results in quantum computing. This includes quantum Fourier transform, quantum simulation of the Schroedinger equation, and the variational quantum eigensolver (VQE) algorithm. During the course students will do one experimental project with entangled photons and one quantum programming project. Students will be guided to implement a quantum algorithm of their choice and run it on a quantum computer (IBM, IonQ, QuEra)

PHYS UN3500 SUPERVISED READINGS IN PHYSICS. 3.00 points.

Prerequisites: the written permission of the faculty member who agrees to act as supervisor, and the director of undergraduate studies permission. Readings in a selected field of physics under the supervision of a faculty member. Written reports and periodic conferences with the instructor

PHYS UN3900 SUPERVISED INDIVIDUAL RESEARCH. 3.00-5.00 points.

Prerequisites: Permission of the departmental representative required. For specially selected students, the opportunity to do a research problem in contemporary physics under the supervision of a faculty member. Each year several juniors are chosen in the spring to carry out such a project beginning in the autumn term. A detailed report on the research is presented by the student when the project is complete

PHYS GU4003 ADVANCED MECHANICS. 3.00 points.

Prerequisites: differential and integral calculus, differential equations, and PHYS UN3003 or the equivalent.
Prerequisites: differential and integral calculus, differential equations, and PHYS UN3003 or the equivalent. Lagranges formulation of mechanics, calculus of variations and the Action Principle, Hamiltons formulation of mechanics, rigid body motion, Euler angles, continuum mechanics, introduction to chaotic dynamics

PHYS GU4011 PARTICLE ASTROPHYS ＆ COSMOLOGY. 3.00 points.

Prerequisites: (PHYS UN1403 or PHYS UN2601 or PHYS UN2802) and (MATH UN1202 or MATH UN1208) students are recommended but not required to have taken PHYS UN3003 and PHYS UN3007.
Prerequisites: (PHYS UN1403 or PHYS UN2601 or PHYS UN2802) and (MATH UN1202 or MATH UN1208) students are recommended but not required to have taken PHYS UN3003 and PHYS UN3007. An introduction to the basics of particle astrophysics and cosmology. Particle physics - introduction to the Standard Model and supersymmetry/higher dimension theories; Cosmology – Friedmann-Robertson-Walker line element and equation for expansion of universe; time evolution of energy/matter density from the Big Bang; inflationary cosmology; microwave background theory and observation; structure formation; dark energy; observational tests of geometry of universe and expansion; observational evidence for dark matter; motivation for existence of dark matter from particle physics; experimental searches of dark matter; evaporating and primordial black holes; ultra-high energy phenomena (gamma-rays and cosmic-rays)

PHYS GU4012 STRING THEORY. 3.00 points.

Prerequisites: PHYS UN3003 and PHYS UN3008 and PHYS GU4021 . PHYS GU4023 would be helpful but is not required. Students should have some familiarity with tools for graphical presentation and numeric problem solving such as Mathematica and/or MatLab.

This course is intended as an introduction to string theory for undergraduates. No advanced graduate-level preparation is assumed, and the material will be covered at (no higher than) the advanced undergraduate level. Advanced topics such as supersymmetry, T-duality, and covariant quantization will not be covered. The focus will be on the dynamics of classical and quantum mechanical strings, with an emphasis on integrating undergraduate material in classical mechanics, relativity, electrodynamics and quantum mechanics.

PHYS GU4018 SOLID STATE PHYSICS. 3.00 points.

Prerequisites: PHYS GU4021 and PHYS GU4023 or the equivalent.
Prerequisites: PHYS GU4021 and PHYS GU4023 or the equivalent. Introduction to solid-state physics: crystal structures, properties of periodic lattices, electrons in metals, band structure, transport properties, semiconductors, magnetism, and superconductivity

PHYS GU4019 MATHEMATICL METHODS OF PHYSICS. 3.00 points.

Prerequisites: PHYS UN3003 and PHYS UN3007 and differential and integral calculus; linear algebra; or the instructor's permission.
Prerequisites: PHYS UN3003 and PHYS UN3007 and differential and integral calculus; linear algebra; or the instructor's permission. This course will present a wide variety of mathematical ideas and techniques used in the study of physical systems. Topics will include: ordinary and partial differential equations; generalized functions; integral transforms; Green’s functions; nonlinear equations, chaos, and solitons; Hilbert space and linear operators; Feynman path integrals; Riemannian manifolds; tensor analysis; probability and statistics. There will also be a discussion of applications to classical mechanics, fluid dynamics, electromagnetism, plasma physics, quantum mechanics, and general relativity

PHYS GU4021 QUANTUM MECHANICS I. 3.00 points.

Prerequisites: PHYS UN3003 and PHYS UN3007
Prerequisites: PHYS UN3003 and PHYS UN3007 Formulation of quantum mechanics in terms of state vectors and linear operators. Three dimensional spherically symmetric potentials. The theory of angular momentum and spin. Identical particles and the exclusion principle. Methods of approximation. Multi-electron atoms

PHYS GU4022 QUANTUM MECHANICS II. 3.00 points.

Prerequisites: PHYS GU4021. Formulation of quantum mechanics in terms of state vectors and linear operators, three-dimensional spherically symmetric potentials, the theory of angular momentum and spin, time-independent and time-dependent perturbation theory, scattering theory, and identical particles. Selected phenomena from atomic physics, nuclear physics, and elementary particle physics are described and then interpreted using quantum mechanical models

PHYS GU4023 THERMAL ＆ STATISTICAL PHYSICS. 3.00 points.

Prerequisites: PHYS GU4021 or the equivalent.
Prerequisites: PHYS GU4021 or the equivalent. Thermodynamics, kinetic theory, and methods of statistical mechanics; energy and entropy; Boltzmann, Fermi, and Bose distributions; ideal and real gases; blackbody radiation; chemical equilibrium; phase transitions; ferromagnetism

PHYS GU4024 Applied Quantum Mechanics. 3 points.

Prerequisites: (PHYS GU4021 and PHYS GU4022)

In this course, we will learn how the concepts of quantum mechanics are applied to real physical systems, and how they enable novel applications in quantum optics and quantum information. We will start with microscopic, elementary quantum systems – electrons, atoms, and ions - and understand how light interacts with atoms. Equipped with these foundations, we will discuss fundamental quantum applications, such as atomic clocks, laser cooling and ultracold quantum gases - a synthetic form of matter, cooled down to just a sliver above absolute zero temperature. This leads us to manybody quantum systems. We will introduce the quantum physics of insulating and metallic behavior, superfluidity and quantum magnetism – and demonstrate how the corresponding concepts apply both to real condensed matter systems and ultracold quantum gases. The course will conclude with a discussion of the basics of quantum information science - bringing us to the forefront of today’s quantum applications.

PHYS GU4040 INTRO TO GENERAL RELATIVITY. 3.00 points.

Prerequisites: PHYS UN3003 and PHYS UN3007 or the equivalent.
Prerequisites: PHYS UN3003 and PHYS UN3007 or the equivalent. Tensor algebra, tensor analysis, introduction to Riemann geometry. Motion of particles, fluid, and fields in curved spacetime. Einstein equation. Schwarzschild solution; test-particle orbits and light bending. Introduction to black holes, gravitational waves, and cosmological models

PHYS GU4050 Introduction to Particle Physics. 3.00 points.

Prerequisites: PHYS UN2601 or PHYS UN2802 or the equivalent.
Prerequisites: PHYS UN2601 or PHYS UN2802 or the equivalent. This course covers the Standard Model of Particle Physics, including it conception, successes, and limitations, with the goal of introducing upper-level physics majors to the foundations and current status of particle physics as a field of research. Specific topics to be covered include: historical introduction and review of the Standard Model; particle interactions and particle dynamics; relativistic kinematics; Feynman calculus, quantum electrodynamics, quantum chromodynamics, and weak interactions; electroweak unification and the Higgs mechanism; neutrino oscillations; and beyond-standard model physics and evidence. Along the way, students will research special topics and familiarize themselves with particle physics research

PHYS GU4051 ADVANCED LABORATORY WORK. 2.00 points.

Prerequisites: the instructors permission. The laboratory has 13 available individual experiments, of which two are required per 2 points. Each experiment requires two (four-hour) laboratory sessions. Registration is limited by the laboratory capacity. May be repeated for credit with different experiment selection. Experiments (classical and modern) cover topics in electricity, magnetism, optics, atomic physics, and nuclear physics

PHYS GU4998 SUPERVISED READINGS. 3.00 points.