Curriculum
Mission Statement
The Physics Department provides education in physics to both undergraduate and graduate students and contributes to the growth of human knowledge through scholarly work.
Program Educational Objectives
The physics department educates students with a program characterized by curricular flexibility, student project work, and active involvement of students in their learning. Through a balanced, integrated curriculum stressing the widely applicable skills and knowledge of physics, we provide an education that is strong both in fundamentals and in applied knowledge, appropriate for immediate use in a variety of fields as well as graduate study and lifelong learning.
Program Outcomes
We expect that physics graduates:
- Know, understand, and use a broad range of basic physical principles.
- Have an understanding of appropriate mathematical methods, and an ability to apply them to physics.
- Have demonstrated oral and written communications skills.
- Understand options for careers and further education, and have the necessary educational preparation to pursue those options.
- Have an ability to learn independently.
- Have acquired the broad education envisioned by the WPI Plan.
- Are prepared for entry level careers in a variety of fields, and are aware of the technical, professional, and ethical components.
- Are prepared for graduate study in physics and/or other fields.
- Can find, read, and critically evaluate selected original scientific literature.
Introduction
Ask a physicist what physics has to do with, and you are likely to be told: "Everything!" Though oversimplified, this answer does contain a kernel of truth. In their study of nature, physicists concern themselves with interactions involving matter and energy of every form.
Physicists' interests range from the tiny world of subatomic particles to stars, galaxies and the vast cosmic sea of space and time in which they travel. They have developed intricate tools to assist the human senses in probing these remote extremes of our natural environment. They have distilled their understanding of nature into laws of great generality and elegance, from the mathematical patterns needed to interpret the perfect symmetry and the regularity of atoms and crystals, to the powerful mathematical treatment of chaos and disorder needed to deal with the concept of heat.
Of course, not all physicists work at the very limits of our knowledge of nature. Many use their understanding of physics to develop practical applications that solve more familiar human problems. The pioneering work on semiconductors in the 1940s led to the development of computers, transistor radios and a communication network that is bringing the peoples of the world ever closer together. The laser, invented in the 1960s, has been used in such varied applications as eye surgery and radar, and even in computerized cash registers. The list of problems solved is long; the list of future possibilities is endless. So there is some truth in the statement that "physics has to do with everything."
One of the distinguishing characteristics of the physicist's approach is a cyclical growth pattern. Systematic experiments provide new facts. New theory is developed to summarize these facts and make them manageable. The new theory has as its consequences practical applications and new questions, leading to new experimentation. Along the way, physicists are guided by certain fundamental principles such as symmetry, continuity and conservation laws.
Students come to the study of physics from many backgrounds and for many reasons. Two aspects in particular seem to attract them. The first is the opportunity to choose from a wide range of intriguing subjects of study, both theoretical and experimental, both fundamental and applied. The second is the combination of intuitive ideas and the penetrating style of logical and mathematical problem-solving which students come to realize physics "has to do with."
Career Opportunities in Physics
Undergraduate physics programs were once formulated with the expectation that graduating students would enter postgraduate programs, where they would earn an advanced degree under the guidance of a practicing physicist. The long-term career objective was assumed to be a permanent position in an academic physics department, with interests divided between scientific research and teaching. Although this traditional outlook is still valid for many students entering the study of physics today, the unprecedented worldwide growth of sciencebased industries has led to exciting new career opportunities involving pure physics mixed with engineering and applied science. Many technically oriented students have also a deep interests in pure science; they are attracted to applied physics because it allows them to satisfy their scientific curiosity while at the same time pursuing the practical objectives of an engineer. In recognition of this new career choice the physics department offers a degree in engineering physics in addition to the traditional physics program. As shown in the sample programs below, students for this degree have great freedom to shape their program to match their individual interests.
Areas of Faculty Interest (Project and Independent Studies)
| P. Aravind | Quantum optics, quantum mechanics, group theory. |
|---|---|
| N. Burnham | Atomic force microscopy, nanomechanics |
| R. Garcia | Condensed matter |
| G. Iannacchione | Calorimetry, liquid crystals |
| S. Jasperson | Optical properties of solids, optical instruments. |
| T. Keil | Solid State Physics, mathematical physics, fluid mechanics. |
| C. Koleci | Physics education research. |
| D. Nelson | Optical and transport properties, solid state physics, lattice dynamics. |
| J. Norbury | Theoretical Nuclear and Particle Physics |
| G. Phillies | Light scattering spectroscopy, complex fluids, biochemical physics. |
| R. Quimby | Optical properties of solids, laser spectroscopy. |
| L. Ram-Mohan | Field theory, many body problems, solid state physics, linear and non-linear optical properties of semiconductors, computational physics. |
| A. Zozulya | Non-linear optics, photo-refractive materials |
Program Distribution Requirements for the Physics and Engineering Physics Majors
The normal period of residency at WPI is 16 terms. In addition to the WPI requirements applicable to all students, completion of a minimum of 10 units of study is required in the areas of mathematics, physics, and related fields as follows:
| Physics Requirements | Minimum Units |
|---|---|
| 1. Mathematics (Note 1). | 3 |
| 2. Physics (including the MQP) (Notes 2, 3). | 5 |
| 3. Other subjects to be selected from mathematics, science, engineering, computer science, and management (Note 3). | 2 |
Notes:
- Mathematics must include at least 2/3 unit of mathematics at the level of MA 3000 or higher.
- ES 3001 and CH 3510 count as physics courses.
- Either item 2 or 3 must include at least 1/3 unit from each of the five principal areas of physics: mechanics, experimental physics, electromagnetism, quantum mechanics, and thermal and statistical physics. This core distribution requirement is satisfied by successfully completing at least one course from each of the following five sets of courses: PH 2201 or 2202 (mechanics); PH 2651 or 2601 (experimental physics); PH 2301 or 3301 (electromagnetism); PH 3401 or 3402 (quantum mechanics); ES 3001, CH 3510, or PH 4206 (thermal and statistical physics); or other courses approved by the department Program Review Committee following petition by the student.
Engineering Physics
- Same requirements as PHYSICS, with the addition that the 10 units must include 2 units of coordinated engineering and other technical/scientific activities. The 2-unit program must be formulated prior to final year of study by the student in consultation with the academic advisor, and must be certified prior to the final year by the departmental Program Review Committee.
Curriculum Outline — Physics and Engineering-Physics
The programs of study described below are designed to fulfill the needs and interests of students over the range from "pure" to "applied," or "engineering" science. They are designed to provide, first of all, a foundation in the indispensable principles and techniques of classical and modern physics. Such preparation is necessary and appropriate for any future in science and technology, including that of postgraduate study and research. Moreover, insofar as appropriate within an undergraduate curriculum, programs are offered which allow options of special experience in some of the active areas of applied or engineering physics.
All programs include a common group of recommended core courses which provide the foundation, beginning with the great themes of physics—matter, motion, forces, energy, and the nature and concepts of electricity and magnetism. They build on that basic knowledge and perspective together with progressively more sophisticated mathematical techniques. Beyond this essential core, a student may choose either a more traditional program of physics study or one relating to an area of individual interest with engineering applications. Illustrations of these options are outlined in the section below, "Physics and Engineering-Physics Programs."
Guidance in the planning of students' programs will be provided by academic advisors. A departmental engineering- physics coordinator is also available for consultation by students and academic advisors on questions pertaining to curriculum and project matters.
In addition to the courses, the Major Qualifying Project (MQP) has the potential to provide valuable experience and to broaden students' perspectives in the chosen subject area—this is one of the exceptional opportunities uniquely associated with the WPI Plan. In the case of students concentrating in one of the engineering-physics fields, the project topic would be chosen for its relevance to that area of interest. Additional information about the MQP is presented in the section on page 178, "Project Opportunities in Physics and Engineering-Physics."
Students who feel that their interests and objectives do not fit naturally into any of the illustrative programs presented here are invited to consult with their academic advisors and with representatives of the Physics Department. It is usually possible to adapt a program to their individual needs.
Physics and Engineering-Physics Programs
For a student entering the study of physics, there is a natural progression of subjects which provide a foundation for advanced work within physics and engineering-physics programs. This constitutes a core sequence which embodies the following indispensable basic areas of study: classical mechanics, electromagnetism, a survey of modern physics, statistical and quantum physics, and laboratory experimental methods. Because the language of the exact sciences is mathematics, there is a parallel core sequence of mathematics courses normally taken either as preparation for or concurrently with the physics courses with which they are paired in the list presented below. In the following table indicates that the mathematics course is strongly recommended; indicates that concurrent study is acceptable.
MA 1021 Calculus I PH 1110 Mechanics
MA 1022 Calculus II PH 1120 Electricity and Magnetism
MA 1023 Calculus III PH 1111 Mechanics
MA 1024 Calculus IV PH 1121 Electricity and Magnetism
MA 1023 Calculus III PH 1130 Introduction to 20th Century Physics
MA 1024 Calculus IV PH 1140 Oscillations and Waves
MA 2051 Differential EquationsPH 2202 Intermediate Mechanics II
MA 2071 Linear Algebra PH 2651 Physics Laboratory
MA 2251 Vector/Tensor CalculusPH 2301 Electromagnetic Fields I
MA 4451 Boundary Value Problems}
(PH 1110, PH 1120)PH 3301 Electromagnetic Theory
PH 3401 Quantum Mechanics I
PH 4206 Statistical Physics
Students needing a somewhat more gradual introduction and an opportunity to gain mathematical skills concurrently are advised to substitute these courses for PH 1111 and PH 1121.
Physics and engineering-physics students should also reserve part of their undergraduate experience for developing perspective in a range of other science and engineering disciplines. A few of the many possibilities are illustrated by the following examples.
- Chemistry (CH 1010, 1030); Material Science (ES 2001). Choosing appropriate materials is often crucial in the development of new experimental techniques that can further our knowledge of physical phenomena. Conversely, the studies of physicists have had profound effects on the development of new materials.
- Electronics, both analog (ECE 2201 and 3204, and digital (ECE 2022). Electronics pervades the modern laboratory. It is valuable to learn electronic principles and designs as they are applied in modern "on-line" experimental data collection and data reduction systems.
- Computer science (CS 1005 and CS 2005). Physics students will need to make skillful use of computers in present and future experimental data processing, theoretical analyses, and the storing, retrieving and displaying of scientific information.
- • Engineering courses related to science. Some basic knowledge in areas such as heat transfer, control systems, fluid mechanics, stress analysis and similar topics will prove to be of great benefit to the physicist called upon to apply professional knowledge to practical engineering problems.
Building on this core and topical subject coverage, physics students are in a position to turn in any number of directions within the range of physics studies, depending on individual interests and career objectives. Six illustrative examples are outlined below. In each case the outline includes a list of recommended and related courses followed by a sampling of project opportunities in the respective areas. Selection of specific courses and projects should be determined by students' interests and the guidance of their academic advisors and the engineering-physics coordinator. For courses outside of the physics department, students are advised to discuss the prerequisites with the instructor.
1. Physics
Recommended Courses
PH 3402 Quantum Mechanics II
PH 4201 Advanced Classical Mechanics
PH (IS/P) Selected Readings in PhysicsRelated Courses
ECE 2311 Continuous-Time Signal and System Analysis
ECE 2312 Discrete-Time Signal and System Analysis
ECE 3801 Advanced Logic Design
ECE 3901 Semiconductor Devices
ES 3011 Control Engineering I
PH 2510 Atomic Force Microscopy
PH 3501 Relativity
PH 3502 Solid State Physics
PH 3503 Nuclear Physics
PH 3504 Optics
PH (IS/P) Modern Optics
PH 501 (Graduate) Mathematical Methods of Physics I
PH 511 (Graduate) Classical Mechanics
MA 4291 Applicable Complex Variables2. Computational Physics.
Recommended Courses
MA 3257 Numerical Methods for Linear and Non-Linear Systems
MA 4411 Numerical Solutions of Differential Equations
PH (IS/P) Numerical Techniques in PhysicsRelated Courses
PH 3402 Quantum Mechanics II
PH 3502 Solid State Physics
PH 501/2 (Graduate)Mathematical Physics
MA 3457/ Numerical Methods for Calculus and CS4033 Differential Equations
MA 4291 Applicable Complex Variables
CS 1101 Introduction to Program Design
CS 2011 Introduction to Computer Organization and Assembly Language
CS 2301 Systems Programming for Non-Majors
CS 4731 Computer Graphics
ECE 2311 Continuous-Time Signal and System Analysis
ECE 2312 Discrete-Time Signal and System Analysis
ECE 3801 Advanced Logic Design
ES 3011 Control Engineering I3. Optics
Recommended Courses
PH 3504 Optics
PH 2501 Photonics
PH 2502 LasersRelated Courses
PH 3402 Quantum Mechanics II
PH 3502 Solid State Physics
PH 542/3 (Graduate) Modern Optics I and II
MA 4291 Applicable Complex Variables
AR/ID 3150 Light, Vision, and Understanding
ECE 2311 Continuous-Time Signal and System Analysis
ECE 2312 Discrete-Time Signal and System Analysis
ES 3011 Control Engineering I4. Electromagnetism
Recommended Courses
PH (IS/P) Modern Optics
PH (IS/P) Selected Readings in ElectromagnetismRelated Courses
PH 3402 Quantum Mechanics II
PH 3502 Solid State Physics
PH 3503 Nuclear Physics
PH 3504 Optics
PH 533 (Graduate) Electromagnetic Theory
PH 514/5 (Graduate) Quantum Mechanics
MA 4291 Applicable Complex Variables
ECE 2311 Continuous-Time Signal and System Analysis
ECE 2312 Discrete-Time Signal and System Analysis
ES 3011 Control Engineering I5. Nuclear Science And Engineering
Recommended Courses
ES 2011 Introduction to Nuclear Technology
PH 3503 Nuclear PhysicsRelated Courses
PH 3402 Quantum Mechanics II
PH 3501 Relativity
PH 553 (Graduate) Nuclear Physics
ME 4832 Corrosion and Corrosion Control
ECE 3801 Advanced Logic Design
ES 3011 Control Engineering I6. Thermal Physics
Recommended Courses
ES 3001 The Statistical Development of Classical Thermodynamics
ES 3004 Fluid Mechanics
PH (IS/P) Selected Readings in Thermal PhysicsRelated Courses
ES 3003 Heat Transfer
ES 3011 Control Engineering I
ME 3410 Compressible Flow
PH 3502 Solid State Physics
PH 3504 Optics
ME 4429 Thermodynamic Applications and Design
ME 4602 Intermediate Fluid Dynamics
PH 501/2 (Graduate) Mathematical PhysicsProject Opportunities in Physics and Engineering-Physics
Opportunities for physics students to participate in theoretical, computer-aided or experimental research exist in numerous fields, including nuclear and particle physics, modern and classical optics, statistical and solid-state physics, electromagnetism, astrophysics, field theories, and in the great range of subfields within these categories.
In the engineering-physics programs, the MQP subject is generally chosen for its relevance to the particular area of concentration. Students usually obtain the assistance of their academic advisors and of the engineering- physics coordinator in arranging the project. It may also include the participation of a project coadvisor who is a member of the engineering faculty.
Information for the selection of a Major Qualifying Project (MQP) by physics and engineering-physics students can be obtained from physics faculty members at any time during the academic year, and especially during the Term C project planning period. A project resource booklet, available in the department office, provides MQP subject information, identification of participating faculty and their areas of interest, and data relating to past projects. Physics faculty serve as project advisors on MQPs in their own fields of research, and sometimes in other appropriate scientific areas of mutual student-advisor interest.
For all physics and engineering-physics students, there are opportunities for off-campus projects in industries, hospitals, research institutions, government and other resources in the Worcester vicinity and beyond. Information on these possibilities, which are constantly changing and expanding, is managed and made available to students and faculty on the Projects Program web site.
Physics for Nonphysics Majors
Physics is the scientific underpinning for all engineering work and is therefore considered by prospective engineers, almost without exception, to be a subject which merits serious study. The elementary physics sequence at WPI encompasses the subject areas of classical mechanics (PH 1110/PH 1111), electricity and magnetism (PH 1120/ PH 1121), 20th century physics (PH 1130), and oscillation and wave phenomena (PH 1140). The sequence is designed to be taken either in the pattern PH 1110, 1120, 1130, 1140, or PH 1111, 1121, 1130, 1140, although other orderings are possible, depending on special circumstances.
The first two courses in this sequence are offered in two versions because of the diversity of backgrounds and preparation of entering students. PH 1111 and PH 1121 are aimed primarily at freshmen with a solid background in the sciences and in mathematics, including calculus. In particular, students in PH 1111 and PH 1121 should be able to differentiate and integrate elementary trigonometric and polynomial functions, and to interpret these operations in graphical form. PH 1110 and PH 1120 are taught at a mathematically less demanding level and are designed for students concurrently beginning their study of calculus, having had little or no college-level calculus preparation in high school.
The courses in classical mechanics and electricity and magnetism are regarded as essential preparation for many fundamental engineering courses as well as for further work in physics.PH 1130 gives a first introduction to 20th century physics: the theory of relativity, quantum physics, nuclear physics and elementary particles. It is designed to provide a context for the appreciation of present-day advances in physics and high-technology applications. PH 1140 deals in depth with oscillations and waves. Engineering applications of this subject reach all the way from LC circuits and electromagnetic wave propagation in electrical engineering to the vibrations of large scale structures such as machinery and highway bridges in mechanical engineering and civil engineering.
There are several intermediate physics courses that may be of interest to nonphysics majors. PH 2201-2202 give a physicist's view of mechanics which to mechanical engineering majors may be an interesting and useful complement to the engineering courses in statics and dynamics. The physics courses in quantum mechanics, PH 3401-3402, and solid state physics, PH 3502, may be of great interest to electrical engineering students specializing in solid state electronics. The courses in electromagnetic field theory, PH 2301 and PH 3301, and optics, PH 3504, would provide a valuable background for students in many areas, such as modern communication systems, fiber optics and optical computing. These are just examples; other courses are also available. For specific information on individual courses, students may consult with the course instructor or with the Physics Department head.
Last modified: February 05, 2008 11:31:13
