# Physics

## Undergraduate Courses

### PH 101X. FRONTIERS AND OPPORTUNITIES IN PHYSICS

Cat. I.

This is a seminar based course intended for students that seek to understand the

breadth of activities, opportunities, and career pathways that are available to students in areas related to physics. Students at any academic level considering PH as a major, both those who are decided as well as those who are undecided, should enroll in PH 101x. The class meets once a week during the fall semester (A & B terms). This course will not substitute for a PH course in the distribution requirements.

### PH 1110. GENERAL PHYSICS-MECHANICS

Cat. I

Introductory course in Newtonian mechanics.

Topics include: kinematics of motion, vectors, Newton's laws, friction, work-energy,

impulse-momentum, for both translational and rotational motion.

Recommended background: concurrent study of MA 1021.

Students many not receive credit for both PH 1110 and PH 1111.

### PH 1111. PRINCIPLES OF PHYSICS-MECHANICS

Cat. I

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.

Recommended background: concurrent study of MA 1023 (or higher).

Students with limited prior college-level calculus preparation are advised to take

PH 1110.

Students may not receive credit for both PH 1111 and PH 1110.

### PH 111X. STUDIO PHYSICS-MECHANICS

Cat. I

Introductory course in Newtonian mechanics taught in a blended studio format. Topics include: kinematics of motion, vectors, Newton's laws, friction, work-energy, impulse-momentum, for both translational and rotational motion. Recommended background: concurrent study of MA 1021. Students may not receive credit for PH 111X and PH 1110 or PH 1111. The recommended follow on physics course is PH 1120.

### PH 1120. GENERAL PHYSICS-ELECTRICITY AND MAGNETISM

Cat. I

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.

Recommended background: working knowledge of the material presented in

PH 1110 or PH 1111 and concurrent study of MA 1022.

Students may not receive credit for both PH 1120 and PH 1121.

### PH 1121. PRINCIPLES OF PHYSICS-ELECTRICITY AND MAGNETISM

Cat. I

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.

Recommended background: 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.

Students may not receive credit for both PH 1121 and PH 1120.

### PH 112X. STUDIO PHYSICS - ELECTRICITY AND MAGNETISM

Introductory course in Electricity and Magnetism.

Topics include: Coulomb’s law, electric field and potential, capacitors, potential difference and current electricity, magnetic fields produced by current-carrying conductors, electromagnetic induction-Faraday’s and Lenz’s laws and their applications.

Recommended background: concurrent study of MA 1021. Students may not receive credit for both PH 112X and PH 1120 or PH 1121.

### PH 1130. MODERN PHYSICS

Cat. I

An introduction to the pivotal ideas and developments of twentieth-century

physics.

Topics include: special relativity, photoelectric effect, X-rays, Compton

scattering, blackbody radiation, DeBroglie waves, uncertainty principle, Bohr

theory of the atom, atomic nuclei, radioactivity, and elementary particles.

Recommended background: 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

Cat. I

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.

Recommended background: 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 115X. 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, Pre-Med, and Pre-Health.

Recommended Background: 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 (MA 1022)

### PH 115X. 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, Pre-Med, and Pre-Health.

Recommended Background: 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 (MA 1022).

### PH 2101. PRINCIPLES OF THERMODYNAMICS

Cat. I

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 free-energies, 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.

Recommended background: introductory mechanics and multi-variable calculus

### PH 2201. INTERMEDIATE MECHANICS I

Cat. 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.

Recommended background: 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

Cat. I

This course is a continuation of the treatment of mechanics started in PH 2201.

Topics covered include: rigid-body dynamics, rotating coordinate systems,

Newton's law of gravitation, central-force problem, driven harmonic oscillator,

an introduction to generalized coordinates, and the Lagrangian and Hamiltonian

formulation of mechanics.

### PH 2301. ELECTROMAGNETIC FIELDS

Cat. I

Introduction to the theory and application of electromagnetic fields, appropriate

as a basis for further study in electromagnetism, optics, and solid-state 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.

Recommended background: introductory electricity and magnetism, vector

algebra, integral theorems of vector calculus as covered in MA 2251.

### PH 2501. PHOTONICS

Cat. II

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 2016-17, 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 2019-20, and in alternating years thereafter .

### PH 2510. ATOMIC FORCE MICROSCOPY

Cat. II

Atomic force microscopes (AFMs) are instruments that allow three-dimensional

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.

Recommended background: PH 1110 and 1120. Suggested background:

PH 1130 and PH 1140.

This course will be offered in 2016-17, and in alternating years thereafter.

### PH 2520. INTRODUCTION TO ASTROPHYSICS

Cat. II

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.

Recommended background is PH 1110 (or PH 1111), PH 1120 (or PH 1121),

and especially PH 1130.

Suggested background: PH 1140.

This course will be offered in 2015-16, and in alternating years thereafter.

### PH 2540. SOLAR SYSTEMS

This course covers physics of the solar system and exo-planetary 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.

Recommended background: a working knowledge of mechanics (PH1110 or 1111), electrodynamics (PH1120 or 1121), modern physics (PH1130), and differential and integral calculus (MA 1021 and MA1022).

### PH 2550. ATMOSPHERIC AND SPACE ENVIRONMENTS

Cat. I

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. Recommended

background: mechanics (PH1010/1011 or equivalent), electromagnetism (PH 1120/1121 or equivalent), and ordinary differential equations (MA 2051 or equivalent).

### PH 2601. PHOTONICS LABORATORY

Cat. II

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.

Recommended background: PH 1110/1111, PH 1120/1121. PH 1130,

PH 1140, and one or more of the courses PH 2501, PH 2502, or PH 3504.

No prior laboratory background is expected.

This course will be offered in 2016-17, and in alternating years thereafter.

### PH 2651. INTERMEDIATE PHYSICS LABORATORY

Cat. I

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 cathode-ray 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 high-quality 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.

Recommended background: the Introductory Physics course sequence or

equivalent. No prior laboratory background beyond that experience is required.

Students who have received credit for PH 2600 or PH 3600 may not receive

credit for PH 2651.

### PH 3206. STATISTICAL PHYSICS

Cat. I

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.

Recommended background: knowledge of quantum mechanics and thermodynamics at the level of ES 3001.

### PH 3301. ELECTROMAGNETIC THEORY

Cat. I

A continuation of PH 2301, this course deals with more advanced subjects in

electromagnetism, as well as the study of basic subjects with a more advanced level

of mathematical analysis. Fundamentals of electric and magnetic fields, dielectric

and magnetic properties of matter, quasi-static time-dependent 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

Cat. I

This course includes a study of the basic postulates of quantum mechanics, its

mathematical language and applications to one-dimensional 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.

Recommended background: Junior standing, MA 4451, and completion of

the introductory physics sequence, including the introduction to the 20th

century physics.

Suggested background: knowledge (or concurrent study) of linear algebra,

Fourier series, and Fourier transforms.

### PH 3402. QUANTUM MECHANICS II

Cat. I

This course represents a continuation of PH 3401 and includes a study of three-dimensional

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.

Recommended background: PH 3401.

### PH 3501. RELATIVITY

Cat. II

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, 4-vectors and tensors, covariance

of the equations of physics, transformation of electromagnetic fields, particle

kinematics and dynamics.

Recommended background: knowledge of mechanics and electrodynamics at

the intermediate level.

This course will be offered in 2016-17, and in alternating years thereafter.

### PH 3502. SOLID STATE PHYSICS

Cat. II

An introduction to solid state physics.

Topics include: crystallography, lattice vibrations, electron band structure,

metals, semiconductors, dielectric and magnetic properties.

Recommended background: prior knowledge of quantum mechanics at an

intermediate level.

Suggested background: knowledge of statistical physics is helpful.

This course will be offered in 2016-17, and in alternating years thereafter.

### PH 3503. NUCLEAR PHYSICS

Cat. II

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.

Recommended background: some knowledge of the phenomena of modern

physics at the level of an introductory physics course and knowledge of

intermediate level quantum mechanics.

This course will be offered in 2015-16, and in alternating years thereafter.

### PH 3504. OPTICS

Cat. II

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.

Recommended background: knowledge of introductory electricity and

magnetism and of differential equations.

Suggested background: PH 2301.

This course will be offered in 2015-16, and in alternating years thereafter.

### PH 350X. OPTICAL PROPERTIES OF SOLIDS

The course will cover the optical physics of solid state materials, including the classical description of optical propagation and reflectivity, quantum treatment of absorption and luminescence, and excitonic effects. The phenomena will be illustrated by discussing the optical properties of insulators, semiconductors, metals, as well as their nanostructures. The course will conclude with a brief introduction to nonlinear optics.

Recommended background: A basic understanding of electricity and magnetism (PH1121 or equivalent), and introduction to quantum mechanics (at level of a modern physics course, PH1130) is recommended.

### PH 443X. INTRODUCTION TO QUANTUM INFORMATION

This course is an introduction to the basic ideas of quantum information. Topics covered will include qubits or two-state quantum systems, physical realizations of qubits, the formalism for treating small numbers of qubits, entanglement and non- locality, gate operations on qubits, the circuit model of quantum computation and some simple quantum algorithms.

Recommended background: Students should have mathematical preparation in ordinary differential equations, vector and tensor analysis, complex variables and linear algebra. In addition, they should have taken an undergraduate course in quantum mechanics (at the level of PH3401 at WPI).

## Graduate Courses

### MPE 510. CLASSICAL MECHANICS

Broad coverage emphasizing interconnections of

a mechanical description of the universe utilizing

both algebraic and calculus language at a level

appropriate for secondary school educators. Topics

include: vectors and vector manipulation to

describe motion, Newton's laws of motion; work

and energy concepts; energy and momentum conservation

laws; models of forces and interactions;

generalized coordinates and momentum; overview

of Lagrangian and Hamiltonian formulations.

### MPE 520. ELECTRODYNAMICS

Broad coverage at the appropriate level emphasizing

interconnections of the electromagnetic

interactions in the universe utilizing both algebraic

and calculus language at a level appropriate for

secondary school educators. Topics include: electro

and magneto statics and dynamics, boundary value

problems; Maxwell's equations; overview

of electromagnetic properties of matter and wave

propagation (radiation).

### MPE 530. MODERN PHYSICS

Broad coverage of the three central areas of

modern physics that emphasize the wonder and

interconnections at the conceptual level appropriate

for secondary school educators. Topics include:

Quantum Physics (postulates, Schrödinger and

Dirac formalisms, implications and interpretations),

Special and Introduction to General

Relativity (the four-vector, space-time, invariants,

time dilation and length contraction), and

Thermo/Statistical Physics (macroscopic variables,

equation of state, state functions, response functions,

microscopic variables, statistical approach,

ensembles, the partition function).

### MPE 540. DIFFERENTIAL EQUATIONS IN NATURE

Emphasizes connections and interconnections

with the mechanical, electromagnetic, and

modern areas as well as mathematical areas of

oscillations, waves, and optics utilizing differential

equations at a level appropriate for secondary

school educators. Topics include: Free, damped,

and driven-damped oscillations, waves, Doppler

Effect, optics, interference and diffraction.

Examples are drawn from a wide range of physical

phenomena to illustrate each concept. To develop

this content, homogeneous and non-homogeneous

differential equations of the first and second

order will be employed. Thick contextual meaning

will be drawn to support mathematical foundation

and vice versa to allow for deeper "authentic"

learning.

### MPE 550. COMPUTATIONAL METHODS IN PHYSICS

Topics are chosen to illustrate various numerical

techniques useful for educators and students to

illustrate physics concepts and develop a sense of

physical intuition through simulations and modeling.

It is not intended to be a course on numerical

methods; rather it will be aimed at the application

of numerical methods to physical models. Various

programming languages/platforms are utilized in

each example to highlight the general nature and

to provide choices matching students' programming

backgrounds.

### MPE 560. EXPERIMENTAL METHODS IN PHYSICS

Hands-on methods of physically testing concepts

and models of the universe. Technology is utilized

but general methods accessible to barely outfitted

lab environments are stressed. Topics covered are

in a series of subject units, the physical principles

underlying the phenomena to be observed and the

basis for the measurement techniques employed

is reviewed. Principles and uses of standard

laboratory instruments (oscilloscopes, meters for

frequency, time, electrical and other quantities,

lock-in amplifiers, etc.) 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 high-quality 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; diffraction-grating

spectroscopy; radioactive decay and nuclear energy

measurements.

### MPE 576. PHYSICS IN POPULAR CULTURE

Covers myths and misconceptions of physics in popular culture (i.e. movies, books, TV, web, etc.).

The goal of this independent study is for the educator

to be able to identify how the representation

of physics in popular media perpetuates important

myths and misconceptions that impact reasoning

and critical thinking, sometimes in a profoundly

negative way. Emphasis is placed on utilizing these

representations as teaching/learning moments for

the specific relevant physical concepts.

### PH 572. NANOSCIENCE JOURNAL CLUB

Students interested in nanoscience read journal articles, write abstracts, give short talks, engage in critical discussion, and provide feedback to fellow students. The objectives of the course are for students to learn about current topics in nanoscience and nanotechnology and to improve their professional skills.

(Prerequisite: A bachelor’s degree in physics, biology, chemistry, or engineering.)

### PH 580. GRADUATE SEMINAR

Students attend Physics Colloquia by WPI faculty and invited scientists on current research topics in different areas of physics. They discuss results and ideas presented in those talks. In addition, students give presentations on their research or on problems of current interest to physics community. The course therefore will provide opportunities for students to develop their presentation skills, broaden their perspectives and provide networking opportunities. All full-time physics graduate students are required to register and attend.