Physics
D. T. PETKIE, HEAD; D. C. MEDICH, ASSOCIATE HEAD
PROFESSORS: P. K. Aravind, N. A. Burnham, G. S. Iannacchione, D. C. Medich, D. T. Petkie, L. R. RamMohan, S. A. Zekavat, A. A. Zozulya
ASSOCIATE PROFESSORS: R. S. Quimby, L.V. Titora, Q. Wen, K. Wu
ASSISTANT PROFESSORS: W.C. McCarthy, R. Trubko
ASSOCIATE PROFESSORS OF TEACHING: R. Kafle, I. Stroe
ASSOCIATE TEACHING PROFESSOR: H. Kashuri
ASSISTANT TEACHING PROFESSORS: S. Kadam, B. Pollard
ASSISTANT RESEARCH PROFESSOR: K. Friedman
INSTRUCTOR OF PHYSICS: T. P. Noviello
ASSOCIATED FACULTY: F. Bernardi (MA), N.A. Deskins (CHE), C. Furlong (ME), D. Lados (ME), B. Tilley (MA), Y. Liu (ME)
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.
 Can find, read, and critically evaluate selected original scientific literature.
 Have an ability to learn independently.
 Understand options for careers and further education, and have the necessary educational preparation to pursue those options.
 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.
The Department of Physics at WPI offers:
 the Bachelor of Science degree in Physics;
 the Bachelor of Science degree in Applied Physics;
 a Minor in Physics;
 a Minor in Astrophysics
The second digit in physics course numbers is coded as follows .
1 — General physics
2 — Theoretical mechanics, statistical physics, kinetic theory, etc . 3 — Electricity and magnetism, electromagnetic theory
4 — Quantum mechanics
5 — Particular topics
6 — Laboratory
INTRODUCTORY PHYSICS SEQUENCE
There are four course topics in the introductory physics sequence . The four topics are Classical Mechanics (PH 1110/PH 1111), Electricity and Magnetism (PH 1120/PH 1121), Modern Physics (PH 1130), and Oscillations and Waves (PH 1140) . Each course includes a laboratory component .
Students should take either PH 1110 or PH 1111, but not both; similarly, either PH 1120 or PH 1121, but not both . The primary difference between the PH 1110PH 1120 option and PH 1111PH 1121 is that the material in
PH 1111 PH 1121 is treated somewhat more formally and rigorously than in PH 1110PH 1120, thus presuming a betterthanaverage mathematics background . The recommended mathematics background for each course is indicated in the respective course description and should be considered carefully in each case .
Because the topics covered in the two mechanics and in the two electricity and magnetism courses are the same, it is possible to cross over from one sequence to the other . For example, PH 1120 could be taken after PH 1111, or, upon consulting with the course instructor, PH 1121 could be taken after successful completion of PH 1110 . Finally, it should be noted that any combination of the first two introductory courses provides adequate preparation for both of the remaining courses in Modern Physics (PH 1130), and Oscillations and Waves (PH 1140) .
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 modern physics and is designed to provide a context for the appreciation of presentday advances in physics and hightechnology applications . PH 1140 deals in depth with oscillating systems, a topic area of fundamental importance in physics, and whose engineering applications span the range from electromagnetic oscillations to the mechanical vibrations of machinery and structures.
PHYSICS AND APPLIED PHYSICS PROGRAMS ADVISING
Because the normal period of residency at WPI is 16 terms (fours terms for four years), there is a potential for 16 units total while the minimum graduation requirement is 15 units. The difference is a WPIwide 1 unit (3 courses) of freeelectives. The general WPI requirements of 4units must include the Humanities and Arts requirement (2 units), the Interactive Qualifying Project – IQP (1 unit), the Social Sciences (2/3 unit), and Physical Education (1/3 unit). For PH and PHA students a minimum of 10 units in the program is required leaving an additional 1unit of physicselectives. Thus, a great deal of flexibility exists to custom craft the curriculum.
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 applied physics programs. This constitutes a core sequence which embodies the following indispensable basic areas of study: classical mechanics, electro magnetism, 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 Modern Physics 
MA 1024 Calculus IV  ↔  PH 1140 Oscillations and Waves 
MA 2051 Differential Equations  ↔  PH 2202 Intermediate Mechanics II 
MA 2071 Linear Algebra  →  PH 2651 Physics Laboratory 
MA 2251 Vector/Tensor Calculus  →  PH 2301 Electromagnetic Fields I 
MA 4451 Boundary Value Problems  ↔ → 
PH 3301 Electromagnetic Theory PH 3206 Statistical Physics PH 3401 Quantum Mechanics I 
Physics and applied 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 “online” experimental data collection and data reduction systems.
 Computer science (CS 1101 or CS 1102 and CS 2301). 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.
 Join Teacher Preparation Program and be armed with leadingedge educator skills and a mastery physics to become a new kind of teacher a teacher who engages and challenges students and makes a difference by educating the next generation of STEM leaders. See the Teacher Preparation program or visit www.wpi.edu/+teach.
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 engineeringphysics coordinator. For courses outside of the physics department, students are advised to discuss the prerequisites with the instructor.
Majors

Applied Physics Major, Bachelor of Science 
Physics Major, Bachelor of Science
Minors
Classes
PH 1110: General Physics—Mechanics
Introductory course in Newtonian mechanics. Topics include: kinematics of motion, vectors, Newton’s laws, friction, workenergy, impulsemomentum, for both translational and rotational motion. Students may not receive credit for both PH 1110 and PH 1111.
concurrent study of MA 1021.
PH 1111: Principles of Physics—Mechanics
An introductory course in Newtonian mechanics that stresses invariance principles and the associated conservation laws. Topics include: kinematics of motion, vectors and their application to physical problems, dynamics of particles and rigid bodies, energy and momentum conservation, rotational motion. Students may not receive credit for both PH 1111 and PH 1110.
concurrent study of MA 1023 (or higher). Students with limited prior collegelevel calculus preparation are advised to take PH 1110.
PH 1120: General Physics—Electricity and Magnetism
An introduction to the theory of electricity and magnetism. Topics include: Coulomb’s law, electric and magnetic fields, capacitance, electrical current and resistance, and electromagnetic induction. Students may not receive credit for both PH 1120 and PH 1121.
working knowledge of the material presented in PH 1110 or PH 1111 and concurrent study of MA 1022.
PH 1121: Principles of Physics—Electricity and Magnetism
An introduction to electricity and magnetism, at a somewhat higher mathematical level than PH 1120. Topics include: Coulomb’s Law, electric fields and potentials, capacitance, electric current and resistance, magnetism, and electromagnetic induction. Students may not receive credit for both PH 1121 and PH 1120.
working knowledge of material covered in PH 1111 and concurrent study of MA 1024 (or higher). Students concurrently taking MA 1022 or MA 1023 are advised to take PH 1120.
PH 1130: Modern Physics
An introduction to the pivotal ideas and developments of twentiethcentury physics. Topics include: special relativity, photoelectric effect, Xrays, Compton scattering, blackbody radiation, DeBroglie waves, uncertainty principle, Bohr theory of the atom, atomic nuclei, radioactivity, and elementary particles.
familiarity with material covered in PH 1110 and PH 1120 (or PH 1111 and PH 1121) and completion of MA 1021 and MA 1022.
PH 1140: Oscillations and Waves
An introduction to oscillating systems and waves. Topics include: free, clamped forced, and coupled oscillations of physical systems, traveling waves and wave packets, reflection, and interference phenomena.
working knowledge of the material covered in PH 1110 and PH 1120 (or PH 1111 and PH 1121) and completion of MA 1021, MA 1022 and MA 1023.
PH 1150: Introductory Physics of Living Systems
This course introduces a selection of physics topics (Thermodynamics, Optics, Fluid Dynamics, Waves, and Atomic and Nuclear Physics) that are critical to students pursuing degrees in Life Sciences, PreMed, and PreHealth.
General Physics Mechanics (PH1110) or Principles of Physics Mechanics (PH1111), General Physics Electricity and Magnetism (PH1120) or Introductory Physics–Electricity and Magnetism (PH1121), completion or concurrent study of Calculus I (MA 1021) or Calculus II (MA1022)
PH 2101: Principles of Thermodynamics
The course provides fundamental preparation for any specialized application of thermodynamics. The material covered includes a general description of large number systems, states, canonical state variables, state functions, response functions, and equations of state. Focus will be given to the physical meanings of freeenergies, enthalpy, chemical potential, and entropy. Connections will be made to equilibrium states, reversible versus irreversible processes, phases and phase transformation, as well as the arrow of time as applied across disciplines.
introductory mechanics and multivariable calculus
PH 2201: Intermediate Mechanics I
This course emphasizes a systematic approach to the mathematical formulation of mechanics problems and to the physical interpretation of the mathematical solutions. Topics covered include: Newton’s laws of motion, kinematics and dynamics of a single particle, vector analysis, motion of particles, rigid body rotation about an axis.
PH 1110, PH 1120, PH 1130, PH 1140, MA 1021, MA 1022, MA 1023, MA 1024 and concurrent registration in or completion of MA 2051.
PH 2202: Intermediate Mechanics II
This course is a continuation of the treatment of mechanics started in PH 2201. Topics covered include: rigidbody dynamics, rotating coordinate systems, Newton’s law of gravitation, centralforce problem, driven harmonic oscillator, an introduction to generalized coordinates, and the Lagrangian and Hamiltonian formulation of mechanics.
PH 2301: Electromagnetic Fields
Introduction to the theory and application of electromagnetic fields, appropriate as a basis for further study in electromagnetism, optics, and solidstate physics. Topics: electric field produced by charge distributions, electrostatic potential, electrostatic energy, magnetic force and field produced by currents and by magnetic dipoles, introduction to Maxwell’s equations and electromagnetic waves.
introductory electricity and magnetism, vector algebra, integral theorems of vector calculus as covered in MA 2251.
PH 2501: Photonics
An introduction to the use of optics for transmission and processing of information. The emphasis is on understanding principles underlying practical photonic devices. Topics include lasers, light emitting diodes, optical fiber communications, fiber lasers and fiber amplifiers, planar optical waveguides, light modulators and photodetectors. Recommended background is PH 1110, PH 1120, PH 1130 and PH 1140 (or their equivalents). This course will be offered in 202223, and in alternating years thereafter.
PH 2502: Lasers
An introduction to the physical principles underlying lasers and their applications. Topics will include the coherent nature of laser light, optical cavities, beam optics, atomic radiation, conditions for laser oscillation, optical amplifiers (including fiber amplifiers), pulsed lasers (Q switching and mode locking), laser excitation (optical and electrical), and selected laser applications. Recommended background is PH 1110, PH 1120, PH 1130 and PH 1140 (or their equivalents). This course will be offered in 202122, and in alternating years thereafter.
PH 2510: Atomic Force Microscopy
Atomic force microscopes (AFMs) are instruments that allow threedimensional imaging of surfaces with nanometer resolution and are important enabling tools for nanoscience and technology. The student who successfully completes this course will understand the functional principles of AFMs, be able to run one, and interpret the data that are collected. This course will be offered in 202122, and in alternating years thereafter. Some sections of this course may be offered as Writing Intensive (WI).
PH 1110 and 1120.
PH 1130 and PH 1140.
PH 2520: Introduction to Astrophysics
A selective study of components of the universe (the solar system, stars, nebulae, galaxies) and of cosmology, based on astronomical observations analyzed and interpreted through the application of physical principles, and organized with the central purpose of presenting the latest understanding of the nature and evolution of the universe. Some topics to be covered include the Big Bang & Inflation; Stellar Behavior & Evolution; White Dwarfs, Neutron Stars, & Supernovae; Black Holes; Dark Matter & Dark Energy. This course will be offered in 202122, and in alternating years thereafter.
PH 1110 (or PH 1111), PH 1120 (or PH 1121), and especially PH 1130.
PH 1140.
PH 2540: Solar Systems
This course covers physics of the solar system and exoplanetary systems. Topics introduced will include the sun, moons and planets; the interplanetary space environment; gravitational interplay, planet atmospheres, surfaces and interiors; interplanetary travel, exploration and habitation; challenges of terraforming, comparison of planetary environments to Earth’s biosphere; and the conditions required to support life. This course will be offered in 202223, and in alternating years thereafter.
a working knowledge of mechanics (PH 1110 or 1111), electrodynamics (PH 1120 or 1121), modern physics (PH 1130), and differential and integral calculus (MA 1021 and MA 1022).
PH 2550/AE 2550: Atmospheric and Space Environments
This course introduces the ambient atmospheric and space environments encountered by aerospace vehicles. Topics include: the sun and solar activity; the solar wind; planetary magnetospheres; planetary atmospheres; radiation environments; galactic cosmic rays; meteoroids; and space debris.
mechanics (PH 1110/1111 or equivalent), electromagnetism (PH 1120/1121 or equivalent), and ordinary differential equations (MA 2051 or equivalent).
PH 2601: Photonics Laboratory
This course provides an experimental approach to concepts covered in Photonics (PH 2501), Lasers (PH 2502), and Optics (PH 3504). Through a series of individually tailored experiments, students will reinforce their knowledge in one or more of these areas, while at the same time gaining exposure to modern photonics laboratory equipment. Experiments available include properties of optical fibers, optical fiber diagnostics, optical communications systems, properties of photodetectors, mode structure and threshold behavior of lasers, coherence properties of laser light, characterization of fiber amplifiers, diffraction of light, polarization of light, interferometry. No prior laboratory background is expected. This course will be offered in 202223, and in alternating years thereafter.
PH 1110/1111, PH 1120/1121. PH 1130, PH 1140, and one or more of the courses PH 2501, PH 2502, or PH 3504.
PH 2651: Intermediate Physics Laboratory
This course offers experience in experimentation and observation for students of the sciences and others. In a series of subject units, students learn or review the physical principles underlying the phenomena to be observed and the basis for the measurement techniques employed. Principles and uses of laboratory instruments including the cathoderay oscilloscope, meters for frequency, time, electrical and other quantities are stressed. In addition to systematic measurement procedures and data recording, strong emphasis is placed on processing of the data, preparation and interpretation of graphical presentations, and analysis of precision and accuracy, including determination and interpretation of best value, measures of error and uncertainty, linear best fit to data, and identification of systematic and random errors. Preparation of highquality experiment reports is also emphasized. Representative experiment subjects are: mechanical motions and vibrations; free and driven electrical oscillations; electric fields and potential; magnetic materials and fields; electron beam dynamics; optics; diffractiongrating spectroscopy; radioactive decay and nuclear energy measurements. Students who have received credit for PH 2600 or PH 3600 may not receive credit for PH 2651.
the Introductory Physics course sequence or equivalent. No prior laboratory background beyond that experience is required.
PH 3206: Statistical Physics
An introduction to the basic principles of thermodynamics and statistical physics. Topics covered include: basic ideas of probability theory, statistical description of systems of particles, thermodynamic laws, entropy, microcanonical and canonical ensembles, ideal and real gases, ensembles of weakly interacting spin 1/2 systems.
knowledge of quantum mechanics and thermodynamics at the level of ES 3001.
PH 3301: Electromagnetic Theory
A continuation of PH 2301, this course deals with more advanced subjects in electromagnetism, as well as study of basic subjects with a more advanced level of mathematical analysis. Fundamentals of electric and magnetic fields, dielectric and magnetic properties of matter, quasistatic timedependent phenomena, and generation and propagation of electromagnetic waves are investigated from the point of view of the classical Maxwell’s equations.
PH 3401: Quantum Mechanics I
This course includes a study of the basic postulates of quantum mechanics, its mathematical language and applications to onedimensional problems. The course is recommended for physics majors and other students whose future work will involve the application of quantum mechanics. Topics include wave packets, the uncertainty principle, introduction to operator algebra, application of the Schroedinger equation to the simple harmonic oscillator, barrier penetration and potential wells.
Junior standing, MA 4451, and completion of the introductory physics sequence, including the introduction to the 20th century physics.
knowledge (or concurrent study) of linear algebra, Fourier series, and Fourier transforms.
PH 3402: Quantum Mechanics II
This course represents a continuation of PH 3401 and includes a study of threedimensional systems and the application of quantum mechanics in selected fields. Topics include: the hydrogen atom, angular momentum, spin, perturbation theory and examples of the application of quantum mechanics in fields such as atomic and molecular physics, solid state physics, optics, and nuclear physics.
PH 3401.
PH 3501: Relativity
This course is designed to help the student acquire an understanding of the formalism and concepts of relativity as well as its application to physical problems. Topics include the Lorentz transformation, 4vectors and tensors, covariance of the equations of physics, transformation of electromagnetic fields, particle kinematics and dynamics. This course will be offered in 202223, and in alternating years thereafter.
knowledge of mechanics and electrodynamics at the intermediate level.
PH 3502: Solid State Physics
An introduction to solid state physics. Topics include: crystallography, lattice vibrations, electron band structure, metals, semiconductors, dielectric and magnetic properties. This course will be offered in 202223, and in alternating years thereafter.
prior knowledge of quantum mechanics at an intermediate level.
knowledge of statistical physics is helpful.
PH 3503: Nuclear Physics
This course is intended to acquaint the student with the measurable properties of nuclei and the principles necessary to perform these measurements. The major part of the course will be an introduction to the theory of nuclei. The principal topics will include binding energy, nuclear models and nuclear reactions. The deuteron will be discussed in detail and the nuclear shell model will be treated as well as the nuclear optical model. This course will be offered in 202122, and in alternating years thereafter.
some knowledge of the phenomena of modern physics at the level of an introductory physics course and knowledge of intermediate level quantum mechanics.
PH 3504: Optics
This course provides an introduction to classical physical optics, in particular interference, diffraction and polarization, and to the elementary theory of lenses. The theory covered will be applied in the analysis of one or more modern optical instruments. This course will be offered in 202122, and in alternating years thereafter.
knowledge of introductory electricity and magnetism and of differential equations.
PH 2301.
PH 4201/PH 511: Advanced Classical Mechanics
A review of the basic principles and introduction to advanced methods of mechanics, emphasizing the relationship between dynamical symmetries and conserved quantities, as well as classical mechanics as a background to quantum mechanics. Topics include: Lagrangian mechanics and the variational principle, central force motion, theory of small oscillations, Hamiltonian mechanics, canonical transformations, HamiltonJacobi Theory, rigid body motion, and continuous systems. This is a 14week course.
PH 2201 and PH 2202.