# Physics

# Physics

The Department of Physics offers courses in physics, experimental physics, mechanics, quantum mechanics, thermodynamics, electricity, waves and optics, thermal and statistical physics, and relativity. The department also offers physics labs.

For questions about specific courses, contact the department:

**Departmental Office:** 704 Pupin

212-854-3348

Office Hours: Monday–Friday, 9:00 a.m.–5:00 p.m.

**Web:** http://www.columbia.edu/cu/physics

## Registration for First-Year Courses

The department offers two beginning sequences in physics:

Physics F1201-F1202; with laboratory, but without calculus as a prerequisite; primarily for premedical students.

Physics C1401-C1403 or Physics C1601-C1602-C2601; three-term sequences, using calculus; primarily for engineering and physical science students. For those students who have had Advanced Placement in physics and calculus, the two-term sequence Physics C2801-C2802 is offered.

**Directory of Classes**

The course information displayed on this page relies on an external system and may be incomplete. Please visit Physics on the Directory of Classes for complete course information.

After finding your course in the Directory of Classes, click on the section number to open an expanded view. The "Open To" field will indicate whether the course is open to School of Professional Studies students. If School of Professional Studies is not included in the field, students may still be able to cross-register for the course by obtaining permission after being admitted to an academic program.

**PHYS BC2001 Physics I: Mechanics. ***4.5 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)., Lab Required

Corequisites: Calculus I or the equivalent.

Fundamental laws of mechanics. Kinematics, Newton's laws, work and energy, conservation laws, collisions, rotational motion, oscillations, gravitation.

Fall 2017: PHYS BC2001 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

PHYS 2001 | 001/01611 | T Th 10:10am - 11:25am Ll104 Diana Center |
Reshmi Mukherjee | 4.5 | 48 |

PHYS 2001 | 002/09888 | T Th 10:10am - 11:25am 903 Altschul Hall |
Reshmi Mukherjee | 4.5 | 6 |

PHYS 2001 | 003/01333 | |
Stiliana Savin | 4.5 | 0 |

PHYS 2001 | 004/04444 | T Th 10:10am - 11:25am 530 Altschul Hall |
Stiliana Savin | 4.5 | 39 |

PHYS 2001 | 005/04667 | T Th 10:10am - 11:25am 530 Altschul Hall |
Stiliana Savin | 4.5 | 3 |

**PHYS BC2002 Physics II: Electricity and Magnetism. ***4.5 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)., Lab Required

Prerequisites: Physics BC2001 or the equivalent.

Corequisites: Calculus II.

Charge, electric field, and potential. Gauss's law. Circuits: capacitors and resistors. Magnetism and electromagnetism. Induction and inductance. Alternating currents. Maxwell's equations.

Spring 2018: PHYS BC2002 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

PHYS 2002 | 001/07410 | T Th 10:10am - 11:25am 405 Milbank Hall |
Janna Levin | 4.5 | 69 |

PHYS 2002 | 002/08240 | T Th 10:10am - 11:25am 405 Milbank Hall |
Janna Levin | 4.5 | 4 |

PHYS 2002 | 003/01696 | |
Stiliana Savin | 4.5 | 9 |

**PHYS BC3001 Physics III: Classical Waves & Optics. ***5 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)., Lab Required

Prerequisites: Physics BC2002 or the equivalent.

Corequisites: Calculus III.

Nonlinear pendula, transverse vibrations-elastic strings, longitudinal sound waves, seismic waves, electromagnetic oscillations & light, rainbows, haloes, the Green Flash; polarization phenomena - Haidinger's Brush, Brewster's angle, double refraction, optical activity; gravity & capillary waves; interference, diffraction, lenses & mirrors.

Fall 2017: PHYS BC3001 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

PHYS 3001 | 001/01361 | T Th 10:00am - 11:30am 510c Altschul Hall |
Timothy Halpin-Healy | 5 | 16 |

PHYS 3001 | 001/01361 | W 4:10pm - 8:00pm 510c Altschul Hall |
Timothy Halpin-Healy | 5 | 16 |

PHYS 3001 | 002/08802 | T Th 10:00am - 11:30am 510c Altschul Hall |
Timothy Halpin-Healy | 5 | 1 |

PHYS 3001 | 003/06186 | W 4:10pm - 8:00pm 510c Altschul Hall |
Timothy Halpin-Healy | 5 | 0 |

**PHYS BC3006 Quantum Physics. ***3 points*.

Prerequisites: BC3001 or C2601 or the equivalent.

Wave-particle duality and the Uncertainty Principle. The Schrodinger equation. Basic principles of the quantum theory. Energy levels in one-dimensional potential wells. The harmonic oscillator, photons, and phonons. Reflection and transmission by one-dimensional potential barriers. Applications to atomic, molecular, and nuclear physics.

Spring 2018: PHYS BC3006 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

PHYS 3006 | 001/07993 | T Th 10:10am - 11:25am 514 Altschul Hall |
Reshmi Mukherjee | 3 | 21 |

**PHYS BC3082 Advanced Physics Laboratory. ***1.5 point*.

Barnard College physics laboratory has available a variety of experiments meant to complement 3000-level lecture courses. Each experiment requires substantial preparation, as well as written and oral presentations. Elementary particle experiments: detectors, cosmic ray triggers, muon lifetime.

**PHYS BC3086 Quantum Physics Laboratory. ***3 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).

Experiments illustrating phenomenological aspects of the early quantum theory: (i) Hydrogenic Spectra: Balmer Series & Bohr-Sommerfeld Model; (ii) Photoelectric Effect: Millikan's Determination of h/e; (iii) Franck-Hertz Experiment; and (iv) Electron Diffraction Phenomena. Substantial preparation required, including written and oral presentations, as well as an interest in developing the knack and intuition of an experimental physicist. This course is best taken concurrently with PHYS BC3006 *Quantum Physics*.

Spring 2018: PHYS BC3086 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

PHYS 3086 | 001/03377 | F 9:00am - 10:00am 510b Altschul Hall |
Reshmi Mukherjee | 3 | 14 |

**PHYS BC3088 Advanced Electromagnetism Laboratory. ***3 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).

Classical electromagnetic wave phenomena via Maxwell's equations, including: (i) Michaelson and Fabry-Perot Interferometry, as well as a thin-film interference and elementary dispersion theory; (ii) Fraunhofer Diffraction (and a bit of Fresnel); (iii) Wireless Telegraphy I: AM Radio Receivers; and (iv) Wireless Telegraphy II: AM Transmitters. Last two labs pay homage to relevant scientific developments in the period 1875-1925, from the discovery of Hertzian waves to the Golden Age of Radio. Complements PHYS W3008 *Electromagnetic Waves and Optics*.

Fall 2017: PHYS BC3088 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

PHYS 3088 | 001/01858 | F 10:30am - 12:00pm 510b Altschul Hall |
Stiliana Savin | 3 | 8 |

**PHYS C1001 Physics for Poets. ***3 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).**Not offered during 2017-18 academic year.**

Prerequisites: No previous background in physics is expected; high school algebra is required.

Introduction to physics with emphasis on quantum phenomena, relativity, and models of the atom and its nucleus. Offered in Spring 2011 only.

**PHYS C1002 Physics for Poets. ***3 points*.

CC/GS: Partial Fulfillment of Science Requirement, BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).**Not offered during 2017-18 academic year.**

Prerequisites: No previous background in physics is expected; high school algebra is required.

Introduction to physics with emphasis on quantum phenomena, relativity, and models of the atom and its nucleus.

**PHYS C1291 General Physics I Laboratory. ***1 point*.

Corequisites: Laboratory to accompany PHYS V1201-2, PHYS V1301-2, or PHYS V1001-2.

**PHYS C1292 General Physics II Laboratory. ***1 point*.

Prerequisites: Laboratory to accompany V1201-2, V1301-2, or V1001-2.

**PHYS C1401 Introduction to Mechanics and Thermodynamics. ***3 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).

Corequisites: MATH V1101 or MATH V1105, or the equivalent.

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.

**PHYS C1402 Introduction to Electricity, Magnetism, and Optics. ***3 points*.

Prerequisites: PHYS C1401, or the equivalent.

Corequisites: MATH V1102 or V1106, or the equivalent.

Electric fields, direct currents, magnetic fields, alternating currents, electromagnetic waves, polarization, geometical optics, interference, and diffraction.

**PHYS C2801 General Physics. ***4 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)., Recitation Section Required

Prerequisites: Advanced placement in mathematics or some knowledge of differential and integral calculus and permission of the departmental representative. (A special placement meeting is held during Orientation Week.)

Mechanics, heat, electricity, magnetism, and light.

**PHYS C2802 General Physics. ***4 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)., Recitation Section Required

Prerequisites: Advanced placement in mathematics or some knowledge of differential and integral calculus and permission of the departmental representative. (A special placement meeting is held during Orientation week.)

Mechanics, heat, electricity, magnetism, and light.

**PHYS UN1001 Physics for Poets. ***3 points*.

CC/GS: Partial Fulfillment of Science Requirement

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.

Spring 2018: PHYS UN1001 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

PHYS 1001 | 001/18801 | M W 2:40pm - 3:55pm 428 Pupin Laboratories |
Szabolcs Marka | 3 | 124/130 |

**PHYS V1201 General Physics I. ***3 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).

Prerequisites: This course will use elementary concepts from calculus. Students should therefore have had some high school calculus, or be concurrently enrolled in MATH V1101.

Corequisites: Taken with accompanying lab PHYS V1291-V1292, the sequence PHYS V1201-C1202 satisfies requirements for medical school.

Mechanics, fluids, thermodynamics.

**PHYS V1202 General Physics II. ***3 points*.

BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).

Prerequisites: This couse will use elementary concepts from calculus. Students should therefore have had some high school calculus, or be cuncurrently enrolled in MATH V1101.

Corequisites: Taken with accompanying lab PHYS V1291-2, the sequence PHYS V1201-2 satisfies requirements for medical school.

Electricity, magnetism, optics, and modern physics.

**PHYS V1900 Seminar in Contemporary Physics and Astronomy. ***1 point*.

Prerequisites: (or corequisite) Any 1000-level course in the Physics or Astronomy departments. This course may be repeated for credit only with the instructor's permission.

Lectures on current areas of research with discussions of motivation, techniques, and results, as well as difficulties and unsolved problems. Each student submits a written report on one field of active research.

**PHYS W1402 Introduction To Electricity, Magnetism, and Optics. ***3 points*.

CC/GS: Partial Fulfillment of Science Requirement

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 W1494 Introduction to Experimental Physics. ***3 points*.

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 W2699 Experiments in Classical and Modern Physics. ***3 points*.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: *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 W3002 From Quarks To the Cosmos: Applications of Modern Physics. ***3.5 points*.

**Not offered during 2017-18 academic year.**

Prerequisites: W2601 or W2802

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 W3018 Weapons of Mass Destruction. ***3 points*.

CC/GS: Partial Fulfillment of Science Requirement, BC: Fulfillment of General Education Requirement: Reason and Value (REA).

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 W4011 Particle Astrophysics and Cosmology. ***3 points*.

**Not offered during 2017-18 academic year.**

Prerequisites: *PHYS W1403*, *W2601* or *W2802*; *MATH V1202* or *V1208*; students are recommended but not required to have taken *PHYS W3003* and *W3007*.

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 W4012 String Theory. ***3 points*.

Prerequisites: *PHYS W3003*, *PHYS W3008*, *PHYS W4021*. *PHYS W4023* 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 W4040 Introduction to General Relativity. ***3 points*.

Prerequisites: *PHYS W3003*, *PHYS W3007* 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 W4050 Introduction to Particle Physics. ***3 points*.

**Not offered during 2017-18 academic year.**

Prerequisites: *PHYS W2601* or *W2802*, or the equivalent.

Review of key concepts in quantum mechanics and special relativity. Conservation laws, decays, interactions, oscillations. Atoms, nuclei, hadrons (protons and neutrons) and quarks. Current theoertical and experimental challenges, including physics at the Large Hadron Collider.

**PHYS W4075 Biology at Physical Extremes. ***0 points*.

Prerequisites: one year each of introductory physics and biology.

This is a combined lecture/seminar course designed for graduate students and advanced undergraduates. The course will cover a series of cases where biological systems take advantage of physical phenomena in counter intuitive and surprising ways to accomplish their functions. In each of these cases, we will discuss different physical mechanisms at work. We will limit our discussions to simple, qualitative arguments. We will also discuss experimental methods enabling the study of these biological systems. Overall, the course will expose students to a wide range of physical concepts involved in biological processes.

**PHYS W4080 Scientific Computing. ***3 points*.

**Not offered during 2017-18 academic year.**

Prerequisites: *PHYS W3003*, *PHYS W3008*, *PHYS W4021*, *PHYS W4023* or the instructor permission.

This course is intended to provide an introduction to scientic computing for Physics and other physical science undergraduates. Methods of computing will be taught through solving a variety of physical science problems. Previous programming experience is useful, but not required. The course will introduce the C++ programming language and also make use of Python and MATLAB in class and in exercises. The first part of the course will introduce these software tools and explore basic numerical algorithms for dierential equations and matrices, emphasizing numerical stability and performance. These algorithms will then be used to explore physical phenomena, such as the equation of state for a simple gas, electromagnetic wave propgation and statistical mechanics systems. A brief discussion of parallel computing techniques will be included, with a chance to implement some parallel algorithms.