### 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

**Assistant Collegiate Professors:** B. Magill and T. R. Merritt

**Instructors:** A. Khan, K. Papavasiliou, and A. L. C. Robinson

**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, biophysics, 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 or biophysics, 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 of astronomy topics ranging from the solar system to the universe, with Application of evidence-based reasoning, critical thinking, and use of theoretical models and observations. 1055 has a focus on the solar system: apparent sky motions, telescopes, matter and radiation, properties of the planets, structure and evolution of the solar system, cultural and intercultural aspects that influenced the understanding of the solar system, climate change as a Global challenge. 1056 has a focus on the universe: stars, star formation, stellar evolution, organization of the Milky Way Galaxy, galaxies, quasars, structure and evolution of the universe, cosmological models, cultural and intercultural aspects of the development of astronomical thought, life in the universe. (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 modern scientific thinking in physics, with application of critical reasoning and quantitative and conceptual problem solving based on fundamental physics principles. Presentation of the key ideas and philosophical aspects of the most important developments in modern physics, such as quantum mechanics, relativity, particle physics, cosmology. Discussion of their impact on our understanding of the universe, our position in it, intercultural aspects, and the relevance of physics for technical challenges requiring global awareness. (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 Newton’s and Einstein’s 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

General physics course sequence for students in curricula other than physical sciences, mathematics, or engineering, who have not studied calculus. Applications of reasoning in the natural sciences using physical laws in a real-world context and in the student’s own discipline. Overview of intercultural and universal aspects of physics, and of human benefits of physics to address global challenges. 2205: mechanics, wave phenomena, fluids. 2206: optics, thermodynamics, electromagnetism, relativity, topics in nuclear and 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

Laboratory experiments dealing with basic laws and techniques of physics; designed to illustrate topics covered in PHYS 2205-2206. Applications of reasoning in the natural sciences using physics experiments in a real-world and interdisciplinary context. Ethical responsibilities and issues in a laboratory setting. 2215: analysis of experimental errors, formatting for presenting graphical data, analyzing and describing and prioritizing experimental design features, communicating concepts orally and in writing, concepts of force, momentum, conservation of energy, wave and interference phenomena. 2216: analysis of experimental errors, communicating concepts orally and in writing, concepts of geometrical optics, optical instruments, heat and phase transitions, electricity and electrical energy storage, magnetic fields and magnetic induction, atomic spectra. Co: 2205 for 2215; 2206 for 2216. (3L,1C)

2305-2306: FOUNDATIONS OF PHYSICS

Introductory sequence for students in physical sciences, mathematics, and engineering. Overview of intercultural contributions to physics and universal aspects of physics, and of human benefits of physics to address world-wide challenges. 2305: classical mechanics of translational and rotational motion, Newtonian gravitation, and thermal physics. 2306: oscillations, waves, electricity, magnetism, and optics. Co: 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)

2324: THERMAL PHYSICS MODULE

Introduction to thermal physics; solids, liquids, and gases; moles, temperature, ideal gas law; work, heat, first law of thermodynamics, ideal gas processes; molecular speeds, pressure; heat engines, refrigerators, the second law of thermodynamics. Intended for transfer students whose introductory physics courses did not include thermal physics. (1H,1C)

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)

2334: WAVES AND SOUND MODULE

Introduction to mechanical waves and sound; one-dimensional waves, transverse waves, sinusoidal waves; sound waves; waves in two- and three-dimensions; power, intensity; the Doppler Effect; principle of superposition of waves; standing waves, standing waves on a string, standing sound waves; interference of waves, interference in two and three-dimensions. Intended for transfer students whose introductory physics courses did not include the topics of mechanical waves and sound. Pre: 2305. (1H,1C)

2344: OPTICS MODULE

Introduction to ray and wave optics; the ray model for light; reflection and refraction; image formation by mirrors; image formation by lenses; lenses in combinations, optical instruments; the wave model of light; interference of light waves; diffraction of light waves. Intended for transfer students whose introductory physics courses did not include introductory optics. Co: 2334. (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, Schrodinger’s 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, Laplace’s equation, and dielectric media. Magnetostatics, magnetic media, and electromagnetic induction. Maxwell’s 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 3406. (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 elicit 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)

4254: QUANTUM INFORMATION TECHNOLOGIES

Quantum computing and other quantum information technologies. Differences between bit and qubit. Quantum logic gates, concept of entanglement, quantum teleportation, quantum cryptography and key distribution, quantum computing algorithms, including Deutsch-Jozsa algorithm, Grover’s search algorithm, Shor’s factoring algorithm. Basics of public-key cryptosystems and number theory as needed to present Shor’s algorithm. Errors in a quantum computer and quantum error correction. Pre: 2306, (MATH 2114 or MATH 2114H). (3H,3C)

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 Einstein’s 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; Einstein’s 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 or ISC 2106H. (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 or CS 1054 or CS 1064 or CS 1114 or ECE 1574 or AOE 2074 or ESM 2074 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.