Director of undergraduate studies: Daniel Prober, 417 BCT, 432-4280, email@example.com; appliedphysics.yale.edu
FACULTY OF THE DEPARTMENT OF APPLIED PHYSICS
Professors Charles Ahn, †Sean Barrett, Hui Cao, Richard Chang (Emeritus), Michel Devoret, Paul Fleury, †Steven Girvin, †Leonid Glazman, Victor Henrich, †Marshall Long, †Tso-Ping Ma, Simon Mochrie, Daniel Prober, Nicholas Read, †Mark Reed, Robert Schoelkopf, †Ramamurti Shankar, †Mitchell Smooke, A. Douglas Stone, †John Tully, Robert Wheeler (Emeritus), Werner Wolf (Emeritus)
Associate Professors †Eric Dufresne, †Jack Harris, Sohrab Ismail-Beigi, †Corey O'Hern, †Hongxing Tang
Assistant Professors Liang Jiang, Peter Rakich
†A joint appointment with primary affiliation in another department.
Physics is the study of the fundamental laws of nature. Applied physics uses these laws to understand phenomena that have practical applications. Engineering in turn makes use of these phenomena for human purposes. Applied physics thus forms a link between the fundamental laws of nature and their applications. Students majoring in Applied Physics take courses in both physics and engineering, as well as courses specifically in applied physics. Students completing the program in Applied Physics are prepared for graduate study in applied physics, in physics, in nanoscience, or in engineering, and, with appropriate prerequisites, in medicine; or they may choose careers in a wide range of technical and commercial fields or in fields such as technical writing or patent law that draw on interdisciplinary subjects.
Contemporary physical science and engineering are becoming increasingly interdisciplinary. Traditional boundaries between fields have blurred, and new areas are constantly emerging, e.g., nanotechnology. The Applied Physics major provides a flexible framework on which students can build a curriculum tailored to their own interests, in consultation with the director of undergraduate studies.
Introductory courses During the freshman year, students interested in Applied Physics should start by taking courses in mathematics, and physics if possible, appropriate to their level of preparation. The choice between different starting points is generally made on the basis of performance on Advanced Placement tests (see the Freshman Web site).
The recommended sequence in mathematics for students interested in Applied Physics or Electrical or Mechanical Engineering is MATH 115, APHY 151, MATH 222, and APHY 194. Either MATH 120 or MATH 230, 231 is an acceptable alternative to APHY 151, and MATH 225 is an acceptable alternative to MATH 222. Similarly, PHYS 301 may be substituted for and MATH 222.
The recommended starting courses in physics are PHYS 200 and 201. These courses should be taken in the freshman year by students who have a strong preparation in mathematics and physics. Students with a particularly strong background in physics and mathematics may take PHYS 260 and 261 instead. Students who are less well prepared in physics and mathematics may choose to take PHYS 180 and 181 during their freshman year, or PHYS 200 and 201 during their sophomore year after they have taken more mathematics courses. Two laboratory courses, such as PHYS 205L and 206L, should be taken at some time during the freshman or sophomore year.
Because computers are ubiquitous in the practical applications of physics, students interested in Applied Physics should also take a course on the use of computers early in their studies. ENAS 130, Introduction to Computing for Engineers and Scientists, is recommended; a comparable course in computer science may be substituted with the approval of the director of undergraduate studies.
The multiplicity of choices facing students interested in this general area indicates the importance of informed advice for freshmen. Students should consult freely with directors of undergraduate studies and individual faculty members in their departments of interest to optimize choices and to ensure maximum flexibility at the time a major is selected.
The major in Applied Physics requires eight courses beyond the introductory sequence. Two of these must be APHY 471, 472. All majors are also required to take APHY 322, 439, and PHYS 420, or equivalents. The three remaining advanced courses should focus on a particular area of concentration. For example, a student interested in solid-state and/or quantum electronics might choose from APHY 321, 448, 449, EENG 320, and 325. A student interested in the physics of materials and/or nanoscience might choose from APHY 448, 449, CHEM 220, 450, and MENG 285. Many other concentrations are possible.
Senior requirement Seniors must complete an independent research project, taken as APHY 471 and 472. The independent research project is under the supervision of a faculty member in Applied Physics, engineering, or the departments of Physics, Computer Science, or Geology and Geophysics. The project may be started in the junior year and continued into the senior year. Students planning to do a research project should contact the project coordinator as early as possible to discuss available options and general requirements.
A well-prepared student interested in materials physics or quantum electronics who starts the senior research in the junior year might elect the following course sequence:
|APHY 151||APHY 194||APHY 439||APHY 448|
|MATH 222||APHY 322||APHY 472||APHY 449|
|PHYS 200||ENAS 130||EENG 320||APHY 471|
|PHYS 201||PHYS 206L||PHYS 420|
A student interested in alternative energy who starts physics in the sophomore year and conducts research in the senior year might elect:
|MATH 115||APHY 194||APHY 322||APHY 448|
|MATH 120||MATH 222||APHY 439||APHY 471|
|PHYS 200||EENG 320||APHY 472|
|PHYS 201||ENAS 130||EENG 406|
|PHYS 205L||PHYS 420|
Approval of programs The Applied Physics major provides for various programs corresponding to a range of student interests. Substitutions of equivalent courses may be permitted. Students interested in an Applied Physics major should contact the director of undergraduate studies as early as possible, and in any case by the end of the sophomore year.
REQUIREMENTS OF THE MAJOR
Number of courses 8 term courses beyond prereqs (incl senior req)
Distribution of courses 3 courses in physical or mathematical sciences or engineering in area of concentration, with DUS approval
Substitution permitted Any relevant course approved by DUS
*APHY 060a or b / ENAS 060a or b / PHYS 060a or b, Energy Technology and Society Daniel Prober
The technology and use of energy. Impacts on the environment, climate, security, and economy. Application of scientific reasoning and quantitative analysis. Intended for non–science majors with strong backgrounds in math and science. Enrollment limited to freshmen. Preregistration required; see under Freshman Seminar Program. QR, SC
TTh 1.00–2.15 Seminar
*APHY 100a or b / ENAS 100a or b / G&G 105a or b / PHYS 100a or b, Energy Technology and Society
The technology and use of energy. Impacts on the environment, climate, security, and economy. Application of scientific reasoning and quantitative analysis. Intended for non–science majors with strong backgrounds in math and science. Enrollment limited to 24. QR, SC
*APHY 110b / ENAS 110b, The Technological World Daniel Prober
An exploration of modern technologies that play a role in everyday life, including the underlying science, current applications, and future prospects. Examples include solar cells, light-emitting diodes (LEDs), computer displays, the global positioning system, fiber-optic communication systems, and the application of technological advances to medicine. For students not committed to a major in science or engineering; no college-level science or mathematics required. Prerequisite: high school physics or chemistry. Enrollment limited to 90. QR, SC
TTh 11.35–12.50 Lecture
APHY 151a or b / ENAS 151a or b, Multivariable Calculus for Engineers Mitchell Smooke [F] and Sohrab Ismail-Beigi [Sp]
An introduction to multivariable calculus focusing on applications to engineering problems. Topics include vector-valued functions, vector analysis, partial differentiation, multiple integrals, vector calculus, and the theorems of Green, Stokes, and Gauss. Prerequisite: MATH 115 or equivalent. QR RP
TTh 9.00–10.15 [F]; TTh 1.00–2.15 [Sp] Lecture
APHY 194a or b / ENAS 194a or b, Ordinary and Partial Differential Equations with Applications Richard Dobbins [F] and Charles Ahn [Sp]
Basic theory of ordinary and partial differential equations useful in applications. First- and second-order equations, separation of variables, power series solutions, Fourier series, Laplace transforms. Prerequisites: ENAS 151 or equivalent, and knowledge of matrix-based operations. QR RP
TTh 9.00–10.15 Lecture
APHY 321bG / EENG 401bG, Semiconductor Silicon Devices and Technology Tso-Ping Ma
Introduction to integrated circuit technology, theory of semiconductor devices, and principles of device design and fabrication. Laboratory involves the fabrication and analysis of semiconductor devices, including Ohmic contacts, Schottky diodes, p-n junctions, solar cells, MOS capacitors, MOSFETs, and integrated circuits. Prerequisite: EENG 320 or equivalent or permission of instructor. QR, SC
MW 9.00–10.15 Lecture
APHY 322b, Electromagnetic Waves and Devices Peter Rakich
Introduction to electrostatics and magnetostatics, time varying fields, and Maxwell's equations. Applications include electromagnetic wave propagation in lossless, lossy, and metallic media and propagation through coaxial transmission lines and rectangular waveguides, as well as radiation from single and array antennas. Occasional experiments and demonstrations are offered after classes. Prerequisites: PHYS 180, 181, or 200, 201. QR, SC
TTh 1.00–2.15 Lecture
APHY 418b / EENG 418b, Heterojunction Devices
A survey of the physics, technology, and fabrication of semiconductor heterojunction materials and devices. Topics include contemporary compound semiconductor material properties and epitaxial growth techniques, high-speed analog and digital devices, microwave and millimeter wave devices for radar and wireless communications, the physics and device properties of quantum wells and superlattices, HEMTs and modulation-doped structures, resonant tunneling physics and devices, and device modeling using computer simulation tools. Laboratory includes fabrication of GaAs FETs and HBTs, fabrication and measurement of quantum Hall effect standards, LEDs, and resonant tunneling devices. Prerequisite: APHY 439a or equivalent. QR, SC
APHY 439aG / PHYS 439a, Basic Quantum Mechanics Robert Schoelkopf
The basic concepts and techniques of quantum mechanics essential for solid-state physics and quantum electronics. Topics include the Schrödinger treatment of the harmonic oscillator, atoms and molecules and tunneling, matrix methods, and perturbation theory. Prerequisites: PHYS 181 or 201, PHYS 301, or equivalents, or permission of instructor. QR, SC
TTh 1.00–2.15 Lecture
APHY 448aG / PHYS 448aG, Solid-State Physics I Liang Jiang
The first term of a two-term sequence covering the principles underlying the electrical, thermal, magnetic, and optical properties of solids, including crystal structure, phonons, energy bands, semiconductors, Fermi surfaces, magnetic resonances, phase transitions, dielectrics, magnetic materials, and superconductors. Prerequisites: APHY 322, 439, PHYS 420. QR, SC
TTh 1.00–2.15 Lecture
APHY 449bG / PHYS 449bG, Solid-State Physics II Michel Devoret
The second term of the sequence described under APHY 448. QR, SC
TTh 2.30–3.45 Lecture
APHY 458aG / PHYS 458aG, Principles of Optics with Applications Hui Cao
Introduction to the principles of optics and electromagnetic wave phenomena with applications to microscopy, optical fibers, laser spectroscopy, and nanostructure physics. Topics include propagation of light, reflection and refraction, guiding light, polarization, interference, diffraction, scattering, Fourier optics, and optical coherence. Prerequisite: PHYS 430. QR, SC
TTh 11.35–12.50 Lecture
*APHY 471a and APHY 472b, Special Projects Daniel Prober
Faculty-supervised individual or small-group projects with emphasis on research (laboratory or theory). Students are expected to consult the director of undergraduate studies and appropriate faculty members to discuss ideas and suggestions for suitable topics. These courses may be taken at any appropriate time in the student's career; they may be taken more than once. Permission of the faculty adviser and of the director of undergraduate studies is required.
HTBA Individual Study