## Undergraduate Courses

### 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 210X. PRINCIPLES OF THERMODYNAMICS

Thermodynamics focuses on the general principles governing the behavior of large ensemble of "things." It answers the basic question, "how do chunks of the universe behave." Because the important aspect is the large number and not the specific "things," this discipline is universally applicable across all length scales and fields of study. The goal is to provide fundamental preparation for any specialty 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 the 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 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 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 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 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 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

Cat. II 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 2015-16, 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.

## Graduate Courses

### PH 511. CLASSICAL MECHANICS

Lagrangian and Hamiltonian formulations. Rigid body motion. Poisson brackets, Hamilton- Jacobi theory. (Prerequisite: B.S. in physics or equivalent.)

### PH 514. QUANTUM MECHANICS I

Schrodinger wave equation, potential wells and barriers, harmonic oscillator, hydrogen atom, angular momentum and spin. (Prerequisite: B.S. in physics or equivalent.)

### PH 515. QUANTUM MECHANICS II

Perturbation theory, scattering theory, Born approximation, quantum theory of radiation, the Dirac equation. (Prerequisite: PH 514.)

### PH 522. THERMODYNAMICS AND STATISTICAL MECHANICS

Ensemble theory; canonical, microcanonical, and grand canonical ensembles. Quantum statistical mechanics, Bose-Einstein and Fermi-Dirac statistics. (Prerequisite PH 511.)

### PH 533. ADVANCED ELECTROMAGNETIC THEORY

Classical electrodynamics including boundary value problems using Green?s functions. Maxwell?s equations, electromagnetic properties of matter, wave propagation and radiation theory. (Prerequisite: B.S. in physics or equivalent.)

### PH 554. SOLID STATE PHYSICS

Phonons and specific heat of solids; electronic conductivity and band theory of solids; Fermi and Bose gases; magnetic interactions. (Prerequisite: PH 514.)

### PH 561. ATOMIC FORCE MICROSCOPY

### PH 597. SPECIAL TOPICS

See the SUPPLEMENT section of the on-line catalog at www.wpi.edu/+gradcat for descriptions of courses to be offered in this academic year.