# Physics

**PHYS C1001y Physics for Poets** *3 pts.* This course
does not fulfill the physics requirement for admission to medical school. No
previous background in physics is expected; high school algebra is required.
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. Science Requirement: Partial
Fulfillment.

**PHYS F1201x-F1202y General Physics** *3 pts.* Prerequisites: Prerequisite for PHYS F1202: PHYS F1201 The course will use elementary concepts from
calculus. Students should therefore have some background in calculus or
should be concurrently taking *MATH V1101, Calculus I*. The accompanying laboratory is
*PHYS W1291-W1292*. Basic introduction to the study of mechanics,
fluids, thermodynamics, electricity, magnetism, optics, special relativity,
quantum mechanics, atomic physics, and nuclear physics.

**PHYS V1201x-V1202y General Physics** *3 pts.* Prerequisites: Prerequisite for PHYS V1202: PHYS V1201 The course will use elementary concepts from
calculus. Students should therefore have some basic background in calculus or
should be concurrently taking *MATH V1101, Calculus I*. The accompanying laboratory is
*PHYS W1291-W1292.* Basic introduction to the study of mechanics,
fluids, thermodynamics, electricity, magnetism, optics, special relativity,
quantum mechanics, atomic physics, and nuclear physics. Science Requirement:
Partial Fulfillment.

**PHYS W1201y General Physics I** *3 pts.* Same course as
*PHYS V1201*, but given off-sequence. The course will
use elementary concepts from calculus. Students should therefore have some
basic background in calculus or should be concurrently taking *MATH V1101, Calculus I*. The accompanying laboratory is
*PHYS W1291*.

**PHYS W1291y General Physics Laboratory** *1 pt.* Same
course as *PHYS W1291*, but given off-sequence. Corequisite:
*PHYS W1201*. This course is the laboratory for the
corequisite lecture course and can be taken only during the same term as the
corresponding lecture.

**PHYS W1291x-W1292y General Physics Laboratory** *1 pt.* Corequisites: PHYS F1201-F1202 or PHYS V1201-V1202. This course is the laboratory for the corequisite
lecture course (*PHYS F1201-F1202* or *PHYS V1201-V1202*) and can be taken only during the same term as
the corresponding lecture.

**PHYS C1401x Introduction To Mechanics and Thermodynamics**
*3 pts.* Corequisite: *MATH V1101*, 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. Science
Requirement: Partial Fulfillment.

**PHYS C1402y Introduction To Electricity, Magnetism, and
Optics** *3 pts.* Prerequisite: *PHYS C1401*. Corequisite: *MATH V1102*, or the equivalent. Electric fields, direct
currents, magnetic fields, alternating currents, electromagnetic waves,
polarization, geometrical optics, interference, and diffraction. Science Requirement: Partial Fulfillment.

**PHYS C1403x Introduction to Classical and Quantum Waves**
*3 pts.* Prerequisite: *PHYS C1402*. Corequisite: *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. Science Requirement: Partial Fulfillment.

**PHYS C1493x Introduction to Experimental Physics** *3
pts.* Prerequisite: *PHYS C1401* and *C1402*. 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 C1493* and *C1494*.

**PHYS C1494y Introduction to Experimental Physics** *3
pts.* Prerequisite: *PHYS C1401* and *C1402*. 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 C1493* and *C1494*.

**PHYS C1601x Physics, I: Mechanics and Relativity** *3.5
pts.* Corequisite: *MATH V1102* or the 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. Science Requirement: Partial Fulfillment.

**PHYS C1602y Physics, II: Thermodynamics, Electricity, and
Magnetism** *3.5 pts.* Prerequisite: *PHYS C1601*. Corequisite: *MATH V1201* or the 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. Science Requirement: Partial Fulfillment.

**ASPH V1900y First-Year Seminar in Contemporary Physics and
Astronomy** *1 pt.* Prerequisite or corequisite: any
*1000*-level course in the Physics or Astronomy Department. May be
taken for Pass/Fail credit only. 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 C2001x or y Special Relativity** *3 pts.* 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 C2601x Physics, III: Classical and Quantum Waves**
*3.5 pts.* Prerequisite: *PHYS C1402* or *C1602*. Corequisite: *MATH V1202* or the 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 C2699y Experiments in Classical and Modern Physics**
*3 pts.* Prerequisites: *PHYS C1601*(or *C1401*), *C1602*(or *C1402*), and *C2601*. Laboratory work associated with the three
prerequisite lecture courses. Experiments in mechanics, thermodynamics,
electricity, magnetism, optics, wave motion, atomic physics, and nuclear
physics.

**PHYS C2801x-C2802y Accelerated Physics, I and II** *4.5
pts.* 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 C1601*, *C1602* and *C2601*, 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 W3081*, in the following year.

**PHYS W3002y From Quarks To the Cosmos: Applications of Modern
Physics** *3.5 pts.**Not offered in 2014-2015.* Prerequisites: C2601 or C2802 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 W3003y Mechanics** *3 pts.* 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 Lagrange's formulation of mechanics, coupled oscillators, and normal
modes.

**PHYS W3007x Electricity and Magnetism** *3 pts.* 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 W3008y Electromagnetic Waves and Optics** *3 pts.* Prerequisite: *PHYS W3007*. Maxwell's 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 W3018y Weapons of Mass Destruction** *3 pts.* 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. Science Requirement: Partial
Fulfillment.

**PHYS W3072y Seminar in Current Research Problems** *2
pts.* Open only to senior physics majors. May be taken ONLY for Pass/Fail
credit, not for letter grade credit. 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.

**PHYS W3081x or y Intermediate Laboratory Work** *2
pts.* Prerequisites: PHYS C2601 or PHYS C2802. Primarily for junior and senior physics majors.
Other majors require the instructor's permission. May be repeated for credit
by performing different experiments. The laboratory has available fifteen
individual experiments, of which two are required per 2 points. 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 W3083y Electronics Laboratory** *3 pts.* Registration is limited to the capacity of the laboratory. Corequisite or
prerequisite: *PHYS W3003* or *W3007*. A sequence of experiments in solid-state
electronics, with introductory lectures.

**PHYS V3500x or y Supervised Readings in Physics** *3
pts.* Prerequisites: the written permission of the faculty member who
agrees to act as supervisor, and the permission of the director of
undergraduate studies. Readings in a selected field of physics under the
supervision of a faculty member. Written reports and periodic conferences
with the instructor.

**PHYS V3900x or y Supervised Individual Research** *1-5
pts.* Prerequisites: the written permission of the faculty member who
agrees to act as supervisor, and the permission of the director of
undergraduate studies. For specially selected physics majors, the opportunity
to do a research project in contemporary physics under the supervision of a
faculty member. A detailed report on the research is presented by the student
when the project is completed.

**PHYS G4003y Advanced Mechanics** *3 pts.* Prerequisites: differential and integral calculus, differential equations,
and *PHYS W3003* or the equivalent. Lagrange's formulation
of mechanics, calculus of variations and the Action Principle, Hamilton's
formulation of mechanics, rigid body motion, Euler angles, continuum
mechanics, introduction to chaotic dynamics.

**PHYS G4011y Particle Physics and Cosmology** Prerequisites:
PHYS C1403, C2601 or C2802; 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 G4018y Solid-State Physics** *3 pts.* Prerequisites: *PHYS G4021* and *G4023*, 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 G4019y Mathematical Methods of Physics** *3 pts.* Prerequisites: Differential and integral calculus; linear algebra; PHYS W3003 and PHYS W3007; or the permission of the instructor. 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 G4021x-G4022y Quantum Mechanics, I and II** *3
pts.* Prerequisite: *PHYS C2601* or *C2802*, or the equivalent, required for *PHYS G4021*; *PHYS G4021* required for *PHYS G4022*. 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 G4023x Thermal and Statistical Physics** *3 pts.* Prerequisite: *PHYS G4021* 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 G4040x Introduction to General Relativity** *3
pts.* 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 G4050y Introduction to Particle Physics** *3 pts.**Not offered in 2014-2015.* Prerequisites: PHYS C2601 or C2802, 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 G4075y Biology at Physical Extremes** 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.