# Physics

The general four-term preengineering physics sequence consists of* PHYS UN1401, UN1402, UN1403, and UN1494 (laboratory); or PHYS UN1601, UN1602, UN2601, and UN2699 (laboratory).*

**PHYS UN1018y Weapons of mass destruction**

*3 pts. Lect: 3. Professor Marka.*

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 UN1401x Introduction to mechanics and thermodynamics**

*3 pts. Lect: 2.5. Professors Zajc and Zelevinsky.*

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

**PHYS UN1402y Introduction to electricity, magnetism, and optics**

*3 pts. Lect: 2.5. Professors Dodd, Hughes, and Zelevinsky.*

Prerequisite: PHYS UN1401. Corequisite: MATH UN1102 or equivalent. Electric fields, direct currents, magnetic fields, alternating currents, electromagnetic waves, polarization, geometrical optics, interference and diffraction.

**PHYS UN1403x Introduction to classical and quantum waves**

*3 pts. Lect: 2.5. Professor Rosen.*

Prerequisite: PHYS UN1402. Corequisite: MATH UN1201 or 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 UN1493x Introduction to experimental physics**

*3 pts. Lab: 3. Members of the faculty.*

Prerequisites: PHYS UN1401 and UN1402. Laboratory work associated with the two prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic and nuclear physics. (Students cannot receive credit for both PHYS UN1493 and UN1494.)

**PHYS UN1494y Introduction to experimental physics**

*3 pts. Lab: 3. **Members of the faculty**.*

Prerequisites: PHYS UN1401 and UN1402. Laboratory work associated with the two prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic and nuclear physics. (Students cannot receive credit for both PHYS UN1493 and UN1494.)

**PHYS UN1601x Physics, I: mechanics and relativity**

*3.5 pts. Lect: 2.5. Professor Humensky.*

Corequisite: MATH UN1102 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 UN1602y Physics, II: thermodynamics, electricity, and magnetism**

*3.5 pts. Lect: 2.5. Professor **Humensky**.*

Prerequisite: 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 UN2601x Physics, III: classical and quantum waves**

*3.5 pts. Lect: 2.5. Professor Dodd.*

Prerequisite: PHYS UN1602 or UN1402. 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 UN2699y Experiments in classical and modern physics**

*3 pts. Lab: 3. Professor Clark.*

Prerequisites: PHYS UN1601 (or UN1401), UN1602 (or UN1402), and UN2601. Laboratory work associated with the three prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic and nuclear physics.

**PHYS UN2801x-UN2802y Accelerated physics, I and II**

*4.5 pts. Lect: 3.5. Rec: 1 hour weekly to be arranged. Professors Mawhinney and Cole.*

Prerequisite: Advanced placement in physics and mathematics, or equivalent, and instructor’s permission. (A special placement meeting is held during Orientation.) This accelerated two-semester sequence covers the subject matter of PHYS UN1601, UN1602, and UN2601 and is intended for 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 UN3002y From quarks to the cosmos: applications of modern physics**

*3.5 pts. Lect: 3.5. Not offered in 2017-2018.*

Prerequisite: PHYS UN2601 or 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 UN3003x Mechanics**

*3 pts. Lect: 2.5. Professor Parsom.*

Prerequisites: General physics; differential and integral calculus. Newtonian mechanics, oscillations and resonance, conservative forces and potential energy, central forces, noninertial frames of reference, rigid body motion, an introduction to Lagrange’s formulation of mechanics, coupled oscillators, and normal modes.

**PHYS UN3007y Electricity and magnetism**

*3 pts. Lect: 2.5. Professor Pasupathy.*

Prerequisite: General physics; 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 UN3008x Electromagnetic waves and optics**

*3 pts. Lect: 2.5. Professor Metzger.*

Prerequisite: PHYS UN3007. 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 UN3081x or y Intermediate laboratory work**

*2 pts. Lab: 2. Members of faculty.*

Prerequisite: PHYS UN2601 or UN2802. 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 15 individual experiments available, 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 UN3083y Electronics laboratory**

*3 pts. Lab: 3. Professor Parsons.*

Registration is limited to the capacity of the laboratory. Corequisite or prerequisite: PHYS UN3003 or UN3007. A sequence of experiments in solid-state electronics, with introductory lectures.

**PHYS GU4003y Advanced mechanics**

*3 pts. Lect: 2.5. Professor Rosen.*

Prerequisites: Differential and integral calculus, differential equations, and PHYS UN3003 or 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 GU4018y Solid-state physics**

*3 pts. Lect: 2.5. Professor Pinczuk and Uemura.*

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

**PHYS GU4019x Mathematical methods of physics**

*3 pts. Lect: 3. Professor Metzger.*

Prerequisites: Differential and integral calculus; linear algebra; PHYS UN3003 and UN3007 or instructor’s permission. Presents a wide variety of mathematical ideas and techniques used in the study of physical systems. Topics 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. Discussion of applications to classical mechanics, fluid dynamics, electromagnetism, plasma physics, quantum mechanics, and general relativity.

**PHYS GU4021x-GU4022y Quantum mechanics, I and II**

*3 pts. Lect: 2.5. Professor Hughes.*

Prerequisite: PHYS UN2601 or UN2802, or
equivalent. Formulation of quantum mechanics
in terms of state vectors and linear operators,
three-dimensional spherically symmetric potentials,
theory of angular momentum and spin, timeindependent
and time-dependent perturbation
theory, scattering theory, and identical particles and
the exclusion principle. Methods of approximation.
Multi-electron atoms. Selected phenomena from
atomic physics, nuclear physics, and elementary
particle physics are described and then interpreted
using quantum mechanical models.

**PHYS GU4023x Thermal and statistical physics**

*3 pts. Lect: 2.5. Professor Denef.*

Pre/Corequisite: PHYS GU4021 or 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 GU4040x Introduction to General relativity**

*3 pts. Lect: 2.5.*

Prerequisites: PHYS UN3003 and UN3007, or 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.