Postbaccalaureate Studies
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.
Departmental Chair: William Zajc
zajc@nevis.columbia.edu
Director of Undergraduate Studies: Jeremy Dodd
dodd@phys.columbia.edu
Departmental Office: 704 Pupin
212-854-3348
Office Hours: Monday-Friday, 9:00 AM-5:00 PM
Web: http://www.columbia.edu/cu/physics
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.
Course scheduling is subject to change. Days, times, instructors, class locations, and call numbers are available on the Directory of Classes.
Fall course information begins posting to the Directory of Classes in February; Summer course information begins posting in March; Spring course information begins posting in June. For course information missing from the Directory of Classes after these general dates, please contact the department or program.
Click on course title to see course description and schedule.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Prerequisite: PHYS C2601 or C2802, or the equivalent. 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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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).
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.
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.
Prerequisite: PHYS C2601 or C2802, or the equivalent. 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.
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.