### Physics

**Chair:** M. L. Pitt

**Professors:** N. Arav, L. N. Chang, J.R. Heflin, J. J. Heremans, P. Huber, J. M. Link, D. Minic, P.R. Montague, S.K. Mun, L. E. Piilonen, M. L. Pitt, M. J. F. Pleimling, E.R. Sharpe, J. H. Simonetti, U. Tauber, and R. B. Vogelaar

**Associate Professors:** S. Economou, G. Khodaparast, C. Mariani, K. Park, H. Robinson, V. W. Scarola, V. Soghomonian, and T. Takeuchi

**Assistant Professors:** L. Anderson, R. Ashkar, E. Barnes, S. Cheng, S. Emori, D. Farrah, J. Gray, S. Horiuchi, V. Nguyen, T. O'Donnell and C. Tao

**Research Faculty:** I. Ozcan and K. Wong

**Adjunct Professors:** C. D. Bowman, Z. Chang, D. Edmonds, R. Li, M. Freedman, Y. Liang, G. R. Myneni, and Z. Toroczkai

**Affiliated Faculty:** L. Asryan^{1}, S. Eubank^{2}, L. Guido^{3}, J. Hanna^{4}, S. Jung^{4}, A. Onufriev^{6} and M. Paul^{7}

**William E. Hassinger, Jr., Senior Faculty Fellow in Physics:** R. B. Vogelaar

^{1}Regular appointment with Material Science and Engineering

^{2}Regular appointment with the Virginia Bioinformatics Institute

^{3}Regular appointment with Materials Science & Engineering and Electrical & Computer Engineering

^{4}Regular appointment with Biomedical Engineering and Mechanics

^{6}Regular appointment with Computer Science

^{7}Regular appointment with Mechanical Engineering

Web: www.phys.vt.edu

### Overview

The physics curriculum is designed to provide a broad foundation in the physical sciences, as well as specialized training in classical and modern physics, and it may lead to either a B.S. or a B.A. An honors student may also qualify for a five-year program leading to both the B.S. and M.S. Experimental opportunities are available in such fields as fundamental particle physics, nuclear physics, condensed matter physics, laser optics, and astronomy. Students are encouraged to participate with faculty members in undergraduate research projects.

Liberal emphases in the physics curriculum permit students to give special attention to those aspects of the discipline they prefer and enable them either to pursue a traditional course of study as preparation for joining the technical staffs of industries or government laboratories, or for graduate studies in physics or astronomy (B.S.); or to pursue an interdisciplinary course of study with a strong background in physics (B.A.).

A handbook that includes sample curricula for emphases in astrophysics, chemistry, computer science, education, electrical engineering, finance, geophysics, materials science, mathematics, physics education, pre-health, and pre-law is available from the department on request.

#### Degree Requirements

The graduation requirements in effect at the time of graduation apply. When choosing the degree requirements information, always choose the year of your expected date of graduation. Requirements for graduation are referred to via university publications as "Checksheets". The number of credit hours required for degree completion varies among curricula. Students must satisfactorily complete all requirements and university obligations for degree completion.

The university reserves the right to modify requirements in a degree program. However, the university will not alter degree requirements less than two years from the expected graduation year unless there is a transition plan for students already in the degree program.

Please visit the University Registrar website at http://registrar.vt.edu/graduation-multi-brief/index1.html for degree requirements.

### Majors

- Physics B.S. (Outstanding students may also elect to complete the requirements for a B.S. "in honors". A description of this honors program in physics is included in the handbook indicated above.)
- Physics B.A.
- Physics B.A. Physics Education Option
- Physics B.A. Pre-Health Option
- Physics B.A. Pre-Law Option

The department also offers the M.S. and Ph.D. in physics (see the Graduate Catalog).

Transfer students should contact the department early, preferably one full semester prior to entrance. This procedure will allow a thorough evaluation of transfer credits and correct placement.

The department participates in the Cooperative Education Program in which a student may alternate through two successive years a semester of study with a semester of professional employment in his/her discipline; these two years normally replace the student's sophomore year. Additional information on the program is included in the "Academics" section in this catalog and in the handbook indicated above.

### Minors

A student may obtain a minor in physics or astronomy by registering with the department and successfully completing the approved minor requirements in effect at the time of graduation. Please visit the University Registrar website at http://registrar.vt.edu/graduation-multi-brief/index1.html for minor requirements.

### Satisfactory Progress

University policy requires that students who are making satisfactory progress toward a degree meet minimum criteria toward the General Education (Curriculum for Liberal Education) (see "Academics") and toward the degree.

Satisfactory progress requirements toward the B.S. and B.A. in Physics can be found on the major checksheet by visiting the University Registrar website at http://registrar.vt.edu/graduation-multi-brief/index1.html.

### Undergraduate Course Descriptions (PHYS)

1055,1056: INTRODUCTION TO ASTRONOMY

Survey course covering astronomy topics ranging from
the solar system to the universe. 1055: apparent sky
motions, telescopes, properties of the planets,
structure and evolution of the solar system.
(3H,3C)

1155,1156: ASTRONOMY LABORATORY

Simulation of apparent sky motions; observations of planets,
stars, and nebulae with quantitative analysis; long term
observations of sky changes; analysis of images; laboratory
experiments of astrophysical relevance.
Co: 1055 for 1155; 1056 for 1156.
(3L,1C)

2074: HIGHLIGHTS OF CONTEMPORARY PHYSICS

Conceptual overview of fundamental modern thinking in
physics. Presents the key ideas and philosophical/ethical
aspects of the most important developments in modern
physics, such as quantum mechanics, relativity, particle
physics, cosmology, etc., and discusses their impact on
our understanding of the universe and our position in it.
(3H,3C)

2114: BLACK HOLES

Properties of black holes and the astronomical evidence for
their existence. Black holes as the most simple objects in
the Universe. Algebra-based physical nature of black holes,
space, time and gravity through Newtonâs and Einsteinâs
theories. Predicted types and properties of black holes,
the deaths of starts, detecting black holes, black holes
in the centers of galaxies, and singularities.
(3H,3C)

2205-2206: GENERAL PHYSICS

For students in curricula other than physical sciences,
mathematics, or engineering, who have not studied calculus.
2205: Mechanics, optics, acoustics. 2206: Electromagnetism,
thermodynamics, relativity, and topics in modern
physics.
Pre: MATH 1016 or MATH 1016H or MATH 1025 or MATH 2015 or MATH 1026 or MATH 1205 or M
ATH 1205H or MATH 1525 or MATH 1535 or MATH 1225 or MATH 1225H for 2205; 2305 or 2205
for 2206.
(3H,3C)

2215-2216: GENERAL PHYSICS LABORATORY

Lab experiments dealing with basic laws and techniques of
physics; designed to illustrate topics covered in General
Physics, 2205-2206. Should be taken concurrently and in
phase with lecture sequence, 2205-2206.
Co: 2205 for 2215; 2206 for 2216.
(3L,1C)

2305-2306: FOUNDATIONS OF PHYSICS I

First two semesters of the three-semester introductory
sequence for students in physical sciences and mathematics.
Includes classical mechanics, gravity, and waves
(2305); heat, electricity, magnetism and optics
(2306); laboratory work. 3304 is the concluding
semester of the sequence. Co: PHYS 2325 or
(MATH 1206 or MATH 1206H or MATH 1226) for
2305.
Pre: (MATH 1205 or MATH 1205H or MATH 1225) or (MATH 1206 or MATH 1206H or MATH 1226)
for 2305; (MATH 1206 or MATH 1206H or MATH 1226), PHYS 2305 for 2306.
(3H,3L,4C)

2325-2326: SEMINAR FOR PHYSICS MAJORS

Introduction to the field of physics and to the Physics
Department. Overview of modern physics topics such as
special relativity, quantum mechanics, condensed matter,
nuclear, and particle physics. Presentation of research
activities in the department. Also provides more in-depth
discussion of and math preparation for topics in 2305-2306.
For physics majors.
Co: 2305 for 2325; 2306 for 2326.
(1H,1C)

2404: PHYSICS OUTREACH

Service learning through teaching. An early field experience
for physics students who are interested in physics
education. Visit local schools and host campus visits
to teach K-12 students fundamental physics concepts
by performing physics demonstrations and activities.
Learn successful communication techniques, lead
classroom discussions, and utilize pedagogical content
knowledge to effectively organize physics presentations
to the general public. Repeatable (no maximum).
Variable credit course.
Co: 2305.

2504: MATH METHODS IN PHYSICS

Applications of mathematical methods to physics. Topics
include spatial coordinate systems, linear algebra
techniques in coupled motions, series approximations of
solutions to physical systems, extremum problems in physics,
differential equations in mechanics, integration in two and
three spatial dimensions, probability theory in thermal
physics. Co: 2306, (MATH 2214 or 2214H) and (MATH
2224 or 2204 or 2204H).
Pre: 2305.
Co: MATH 2214, MATH 2224, 2306.
(3H,3C)

2964: FIELD STUDY

Pass/Fail only. Variable credit course.

2974: INDEPENDENT STUDY

Variable credit course.

2974H: INDEPENDENT STUDY

Honors section.
Variable credit course.

2984: SPECIAL STUDY

Variable credit course.

2994: UNDERGRADUATE RESEARCH

Variable credit course.

2994H: UNDERGRADUATE RESEARCH

Honors
Variable credit course.

3154: OBSERVATIONAL ASTROPHYSICS

Telescopic observations of the moon, planets, stars,
interstellar medium, and galaxies; astrophotography; digital
imaging. Telescopes; virtual observing techniques and
instruments; photographic and digital imaging systems.
Astronomical data reduction and interpretation; digital
image processing. Prior credit for Phys 2154 precludes
credit for 3154.
Pre: 1156.
(1H,3L,2C)

3254: ENRICHED PHYSICS OUTREACH

Design and implementation of physics lesson plans for K-12
students at local schools and campus visits. Creation of
inquiry-based, student-centered physics lessons which
motivate and educate students of all ages. Development
of activities and experiments to engage students in being
scientists.
Co: 2306.
(3H,3C)

3314: INTERMEDIATE LABORATORY

Characteristics of common instrumentation and basic
circuits, methods of producing good practices in data
gathering, recording, and analysis.
(2H,3L,3C)

3324: MODERN PHYSICS

Photons and their interactions with matter, wave-particle
duality, Heisenberg uncertainty principle, Schrodingerâs
equation of motion, hydrogenic and multi-electron atoms,
Pauli exclusion principle, molecules, solids, nuclei,
elementary particles. Includes lab work. MATH 4544 can be
substituted for co-requisite MATH 2214 or 2214H.
Co: 2504, MATH 2214 or MATH 2214H.
Pre: 2306.
Co: MATH 2214, 2504.
(3H,3L,4C)

3355-3356: INTERMEDIATE MECHANICS

Formal aspects of classical mechanics and dynamics.
Topics include Newtonian, Lagrangian and Hamiltonian
theory applied to non-relativistic systems in one, two,
and three dimensions, relativistic dynamics, linear algebra
applied to coupled many-body motion, small oscillations,
and rigid body motion.
Pre: (MATH 1224 or MATH 2204 or MATH 2204H), (MATH 2214 or MATH 2214H), PHYS 2305, PHYS 2306, PHYS 2504 for 3355; 3355 for 3356.
(3H,3C)

3405-3406: INTERMEDIATE ELECTRICITY AND MAGNETISM

Electrostatics, multipoles, Laplaceâs equation, and
dielectric media. Magnetostatics, magnetic media, and
electromagnetic induction. Maxwellâs equations,
electromagnetic energy, waves, and radiation.
Must meet pre-requisites and have a grade of C or better
in each of 2305-2306 sequence.
Pre: (MATH 2214 or MATH 2214H), PHYS 2305, PHYS 2306, PHYS 2504 for 3405; 3405 for 34
06.
(3H,3C)

3655,3656: INTRODUCTION TO ASTROPHYSICS

Application of elementary physical laws to determine
dimensions, masses, luminosities, structures, and evolution
of astronomical objects and the universe as a whole.
Emphasis is on quantitative derivation.
Pre: 2306.
(3H,3C)

3704: THERMAL PHYSICS

Introduction to the concepts, formalism, and applications
of classical and quantum statistical mechanics, including
thermodynamics. Co: 2504, (MATH 2214 or 2214H).
Pre: 2306, 3324.
Co: MATH 2214, 2504.
(3H,3C)

4224: PHYSICS TEACHING AND LEARNING

Seminar course on how people learn and understand
key concepts in physics to encourage more effective
teaching strategies. Discussions of readings in physics,
physics education research, and cognitive science.
Recognition of common student preconceptions of
physics concepts and identification of strategies which
help to elict conceptual change. Field work teaching
precollege or college students. For students interested
in teaching and learning physics, graduate teaching
assistants, and undergraduate learning assistants.
Pre: 2306.
(2H,2C)

4315-4316: MODERN EXPERIMENTAL PHYSICS

Representative apparatus, techniques, and phenomena of
contemporary research. Includes electrical measurements,
computers, thermometry, vacuum deposition, machine shop,
nuclear spectra, experimentation related to major
developments of modern physics.
Pre: 3314 for 4315; 3314, 4315 for 4316.
(6L,2C)

4455-4456: INTRODUCTION TO QUANTUM MECHANICS

Experimental bases; postulates; conservation theorems and
symmetry; one-dimensional and two-dimensional problems;
angular momentum and problems in three dimensions; matrix
mechanics and spin; applications to atomic and molecular
physics; perturbation theory; scattering.
Pre: 3356 for 4455; 4455 for 4456.
Co: 3406 for 4455.
(3H,3C)

4504: INTRODUCTION TO NUCLEAR AND PARTICLE PHYSICS

Structure and properties of atomic nuclei and elementary
particles, theoretical interpretations based on elementary
quantum mechanics. Symmetries; various nuclear models;
interactions at small distances; classification of
elementary particles. Consent required.
Co: 4456.
(3H,3C)

4554: INTRODUCTION TO SOLID STATE PHYSICS

Basic concepts of solid state physics including crystal
structure, lattice vibrations, electron states, energy
bands, semiconductors, metals. Consent required.
Co: 4456.
(3H,3C)

4564: POLYMER PHYSICS

Introduction to the field of polymer physics. Statistical
descriptions of polymers based on Brownian motion and
random walk models. Conformations and single chains.
Thermodynamics of polymer mixtures, solutions, and melts.
Properties of polymer networks. Polymer dynamics in both
melt and solution states.
Pre: 2306.
(3H,3C)

4574: NANOTECHNOLOGY

Introduction to methods of controlling matter on the
nanometer length scale and the applications thereof.
Nanolithography, self-assembly, and scanned probe
microscopy; nanomaterials including fullerenes, carbon
nanotubes, and quantum dots; nanoscale and molecular
electronics; nanoelectromechanical systems; nanoscale
optoelectronics; and nanobiotechnology.
Pre: 2205, 2206 or 2305, 2306.
(3H,3C)

4614: OPTICS

Fundamentals of the ray, wave and quantum models of light,
and topics in modern optics with contemporary applications.
Pre: 2306, MATH 2214, (MATH 2224 or MATH 2204 or MATH 2204H).
(3H,3C)

4624: OPTICS LABORATORY

Laboratory experiments dealing with ray and wave optical
phenomena designed to illustrate and complement the
principles covered in OPTICS Phys 4614. Physics majors are
required to take 4624 concurrently with the lecture course
4614.
Co: 4614.
(3L,1C)

4654: MODERN COSMOLOGY

Survey of our current understanding of the origin,
evolution, and fate of the Universe. Observational evidence
behind the idea of the hot Big Bang, including the linear
velocity-distance law, the existence of the cosmic microwave
background, and the arguments for dark matter. Physics of a
dynamic, expanding Universe via the Friedman-Lemaitre-
Robertson-Walker metric. Physical principles to determine
the conditions in the early Universe, introducing the idea
of inflation. Mechanisms driving the origin and evolution of
galaxies and large-scale structures.
Pre: 3656.
(3H,3C)

4674: INTRODUCTION TO GENERAL RELATIVITY

Introduction to methods and applications of Einsteinâs
general theory of relativity. Space and time and gravity in
Newtonian physics; special theory of relativity, gravity
as geometry of curved space-time; black holes; cosmology;
Einsteinâs gravitational field equations; gravitational
waves and relativistic stars.
Pre: MATH 2214 or MATH 2214H or MATH 2514, PHYS 3356.
Co: 3406.
(3H,3C)

4714: INTRODUCTION TO BIOPHYSICS

Selected topics from the general area of biomechanics,
bioelectricity, radiation biophysics, molecular biophysics,
and thermodynamics and transport in biological systems.
Emphasis on the physical aspects of biological phenomena
and biophysical measurement techniques and instrumentation.
Pre: 2206 or 2306.
(3H,3C)

4755-4756: INTRODUCTION TO COMPUTATIONAL PHYSICS

Survey of computational methods in physics.
4755: Applications in physics of curve fitting, numerical
calculus, ordinary and partial differential equations,
numerical methods for matrices, spectral analysis, and
N-body systems. 4756: Investigation of physical systems
using Molecular Dynamics simulations, Monte Carlo
simulations, genetic algorithm and numerical
renormalization. Introduction to advanced techniques, as
for example density matrix renormalization group method,
matrix product state approach, smoothed particle
hydrodynamics, and density functional theory.
Pre: 2306, CS 1044 for 4755; 4455, 4755 for 4756.
(3H,3C)

4774: INTRO TO PHYSICS OF GALAXIES

Survey of our current observational and theoretical
understanding of the formation and evolution of galaxies.
Observational review of galaxy sizes and compositions,
including the origin of the Hubble sequence. Physical
description of a galaxy via distribution functions and
stellar orbits. Time evolution of the distribution function.
The Schwarzschild method for determining orbits.
The physics of active galaxies.
Pre: 3656.
(3H,3C)

4964: FIELD STUDY

Pass/Fail only. Variable credit course.

4974: INDEPENDENT STUDY

Variable credit course.

4974H: INDEPENDENT STUDY

Honors section.
Variable credit course.

4984: SPECIAL STUDY

Variable credit course.

4994: UNDERGRADUATE RESEARCH

Variable credit course.

4994H: UNDERGRADUATE RESEARCH

Honors section.
Variable credit course.