Computational Physics for Upper Level Courses
Contributed Abstracts
Email abstracts to Wolfgang Christian at Davidson College.

OSP Quantum Mechanics: Interactive Computer-Based Curricular Material
Mario Belloni and Wolfgang Christian, Department of Physics, Davidson College

We have produced and class-tested interactive Open Source Physics-based curricular material in support of introductory, intermediate, and advanced courses in quantum mechanics. These exercises address both quantitative and conceptual difficulties encountered by many students in such topics as energy-eigenfunction shape, momentum space, time evolution, and classical/quantum-mechanical correlations. Because the materials are extremely flexible, these exercises are appropriate for use with a variety of levels and pedagogies. Examples of the curricular materials, the results of our preliminary assessment of their effectiveness, and future directions of this project will be discussed. [Poster PDF]

Open Source Physics is supported in part by the National Science Foundation (DUE-0442581)

Eddy Current Simulations Using the Receding Image Method
Yao Liu, Columbia University
John Belcher, Massachusetts Institute of Technology

We present a number of ways to view the magnetic fields and eddy currents in the Arago's disk experiment in which a magnet is levitated above a moving conductor by induced eddy currents. The mathematics of the computation is well known (W. M. Saslow, Am. J. Phys. 60, (8), 693, 1992). Our emphasis here is on the presentation of the mathematical solution using an interactive 3D applet and movies made using Sundquist's Dynamic Line Integral Convolution method to display time varying fields.

This work is supported in part by the National Science Foundation (DUE 0618558).

Combining Computational Physics with Video Analysis in Tracker
Douglas Brown, Department of Physics, Cabrillo College

In Spring 2007, introductory mechanics students at Cabrillo College used Tracker to compare 2D particle models with videos of real-world motion. After doing a traditional motion video analysis lab, students used both analytic (position functions) and dynamic (force functions and initial conditions for numerical solvers) models to draw overlays directly on their captured videos. The video thus provided a "reality check" while students explored different models, parameters and algorithms. In addition to the visual overlays, the models generated "experimental data" for graphing and analysis just like experimental (student-marked) tracks. This paper will describe my own and my students' experiences with this first exposure to computational physics in the curriculum. Tracker is a JAVA video/image analysis tool developed by the Open Source Physics Project. [Poster PDF]

*Curricular development supported in part by the National Science Foundation grants DUE-0126439 and DUE-0442481.

Computational Course Projects and Undergraduate Research
Brian Clark and Richard F. Martin, Department of Physics, Illinois State University

As part of our undergraduate degree sequence in computational physics at Illinois State University we offer a senior level projects course and a capstone computational research course. In the projects course students are introduced to three different types of numerical simulations and are asked to write their own codes to implement each type, applied to a specific problem in physics or a related area. Example projects over the past six years include the finite element method applied to heat transport in solids, the split-operator technique applied to time-dependent wave packet evolution, a Monte Carlo simulation of photon scattering in a turbid medium, and a neural network used to predict time series such as that of the auroral electroject geomagnetic index. For the capstone research course, students can choose to work on a computational project of their own design or one suggested by a faculty member, and these projects have ranged over a variety of topics in physics and other disciplines. In this presentation we will discuss several selected recent projects from these classes and how they are often suggested by and/or lead to extracurricular research topics in which students and faculty are involved. In this way research is intrinsically linked to the computational physics curriculum.

Computation in the Lawrence Physics Curriculum
David M. Cook, Department of Physics, Lawrence University

The physics curriculum at Lawrence University introduces on-line data acquisition, statistical data analysis, and curve fitting in the introductory laboratories; includes the required course Computational Mechanics in which sophomores learn to use computer-based symbolic, numerical, and visualization tools to address intermediate mechanics problems that involve ordinary differential equations, integrals, eigenvalues, and eigenvectors; and offers the junior-senior elective Computational Physics that focuses on numerical solution of the wave, diffusion, and Laplace equations by finite difference and finite element methods. Because Computational Mechanics is prerequisite for most upper-level courses, faculty members can as appropriate assign computer-based exercises in those courses. Further, students are encouraged to use our Computational Physics Laboratory on their own initiative whenever that use seems appropriate. Details about the Lawrence curricular approach and about the microscopically customizable text that used for some of its components are posted on the web site at and are recorded in an 82-page report published in December, 2006, having the same title as this poster and available electronically at the indicated web site and in hard copy from the author.

*Curricular development supported in part by the W. M. Keck Foundation, the National Science Foundation, and Lawrence University.

Computation in Classical Mechanics
Javier E. Hasbun, Department of Physics, University of West Georgia

Scientific advances create the need to become computationally adept to tackling problems of increasing complexity. The use of computers in attaining solutions to many of science's difficult problems is inevitable. Therefore, educators face the challenge to infuse the undergraduate curriculum with computational approaches that will enhance students' abilities and prepare them to meet the world's newer generation of problems. Computational physics courses are becoming part of the undergraduate physics landscape and learned skills need to be honed and practiced. A reasonable ground to do so is the standard traditional upper level physics courses. I have thus developed a classical mechanics textbook (1) that employs computational techniques. The idea is to make use of numerical approaches to enhance understanding and, in several cases, allow the exploration and incorporation of the "what if environment" that is possible through computer algorithms. The textbook uses Matlab because of its simplicity, popularity, and the swiftness with which students become proficient in it. The example code, in the form of Matlab scripts, is provided not to detract students from learning the underlying physics. Students are expected to be able to modify the code as needed. Efforts are under way to build OSP (2) Java programs that will perform the same tasks as the scripts. Selected examples that employ computational methods will be presented.    [Poster PDF]
(1) To be published, Jones and Bartlett Publishers.
(2) Open Source Physics:

Moving Reluctant Students and Faculty over the Computational Algebra Hurdle
Randall S. Jones and Joseph Ganem, Loyola College in Maryland

Computer algebra systems such as Mathematica open up an entirely new dimension of learning and teaching opportunities for advanced physics courses. Unfortunately, the learning curve for these systems is such that students and some faculty members are reluctant to embrace them. One approach is to convince both groups that these are valuable tools in helping to solve traditional end-of-chapter problems in the early, advanced physics courses. This can be accomplished by simply providing homework solutions that include explicit computational algebra work. With a little extra work these solutions can be worked into the format of a tutorial. After becoming comfortable with the algebra system in this format, both groups can move more comfortably toward addressing advanced applications. Examples from the first semester of quantum mechanics will be provided.

System Dynamics Markup Language: An open source modeling toolkit
David Joiner, New Jersey Center for Science and Technology Education, Union NJ, USA

System dynamics is a modeling technique where systems of coupled ordinary differential equations are expressed graphically in terms of stocks, flows, and connections. System dynamics models are drawn in a manner similar to flowcharts, and existing software lets scientists directly solve models from these diagrams. Commercial packages are currently available, but there are a lack of open source packages in the scientific community. We present initial development of an open- source systems dynamics modeling environment. An XML schema (System Dynamics Markup Language, SDML) has been developed to describe and share system dynamics models. Additionally, a software tool (SDMLBrowser) has been developed in Java to graphically create, run, and visualize the results of systems dynamics models.

Dissemination of Animation-Based Curricular Materials: BQ Database
William F. Junkin III and Anne J. Cox, Eckerd College

This poster describes the design and development of a database and an associated website for disseminating computational-based animations and the accompanying curricular materials ( The audience should range from users to contributors, i.e., from students or teachers using materials 'as is' to people who delight in computer programming. The primary design considerations are ease of use, of searching, of organization, of editing or customizing prior submissions, and of submitting new resources. We also worked closely with the ComPADRE digital library so that a search of ComPADRE could include a seamless search of the BQ Database. This poster will describe the design of the website and its database used to reach these goals. [Poster PDF]

Open Source Physics is supported in part by the National Science Foundation (DUE-0442581)

Computation in the Paradigms Curriculum at Oregon State University
David McIntyre, Oregon State University

Paradigms in Physics is a novel upper-division physics curriculum developed at Oregon State University. The junior year comprises ten modular courses, each focused on a specific paradigm or class of physics problems that serves as the centerpiece of the course and on which different tools and skills are built. A variety of computational examples and exercises are used throughout the courses. Our students are comfortable with computational techniques and tools since they take a required introductory computational physics course that also acts as a gateway for our Computational Physics degree program. We use Maple, Mathematica, Java, and other software packages to help students do calculations, visualize graphics, and perform simulations. In particular, we have developed a Java version of a program to simulate Stern-Gerlach spin 1/2 experiments that forms an integral part of our first quantum mechanics Paradigm course. This program has recently been integrated into the Open Source Physics framework by the Davidson group. These and other examples from our curriculum will be presented.

WebTOP: Three Dimensional Interactive Simulations and Activities for Teaching and Learning Waves and Optics
Taha Mzoughi, Kennesaw State University and John T. Foley, Mississippi State University

WebTOP is a 3D interactive computer graphics system developed to help instructors teach and students learn about waves and optics. WebTOP modules span nine different subject areas: waves, geometrical optics, reflection and refraction, polarization, interference, diffraction, lasers, scattering and modern physics. Each module has an interactive simulation, a theory section, sets of examples and exercises, and a scripting feature for recording interactions. In addition, WebTOP includes several highly interactive guided tutorials. WebTOP simulations are written in VRML 2.0, Java and the External Authoring Interface (EAI.) We are currently working on porting the code into X3D. Current plans include also making the code open source. WebTOP is sponsored in part by the National Science Foundation (DUE 0231217).

The Monte Carlo Method in Undergraduate Statistical Mechanics
Kelly Roos, Bradley University

Monte Carlo (MC) simulation techniques are invaluable in enhancing undergraduate physics students' understanding of the fundamentals of statistical mechanics. In the statistical mechanics course I have taught at Bradley University I have made learning and applying MC simulations an integral part of the course. I will demonstrate how, beginning with a simple application of the Metropolis algorithm to simulate a random walk, I guide the students to incrementally add to their simulation through assignments and projects to ultimately produce sophisticated MC simulations of various complex physical systems.

Visualizing Tensors
Rob Salgado, Syracuse University

We present a visualization of the tensor algebra of vectors and differential-forms, inspired by Schouten's "Tensor Calculus for Physicists", Burke's "Applied Differential Geometry", and Misner-Thorne-Wheeler's "Gravitation". In particular, we visualize the operations of addition, inner-product, outer-product, index-raising and -lowering, and Hodge-dual. These visualizations may be useful in the teaching of tensors in advanced physics courses. We provide some physical examples from electrodynamics and relativity. We also demonstrate software being developed in VPython and in Maple to visualize tensorial computations.  [Poster PDF] [Website]

Interdisciplinary Cluster Computing at a Liberal Arts College
David Schaich, Scott Kaplan, William Loinaz and James Hagadorn, Boston University

Research in computational science often requires substantial processing and data storage resources, which may not be easily accessible to undergraduates. Amherst College is constructing a high-performance scientific computing cluster to be used for such computationally intensive research as well as training in computational science and parallel processing. Since coming online in 2006, the cluster has been used by undergraduate and faculty researchers in physics, computer science, geology, chemistry, biology and statistics, including four undergraduate honors theses. The cluster has also spurred the development of a new course in computational science, to be offered jointly by the Computer Science and Physics Departments for the first time in 2007-2008.  [Poster PDF]

Creating a Computational and Visualization Laboratory
Jim Socacki, James Madison University

In 1996 faculty from the Departments of Physics and Mathematics at James Madison University and North Carolina Central University collaborated on creating a computational science program. This collaboration led to us submitting an NSF proposal. In 1999 NSF funded our proposal, which at that time was centered around fluid mechanics. The program consists of joint classes between the two departments and the two universities. Students majoring in Physics, Mathematics and Computer Science can get a concentration in computational science by taking courses in the curriculum.

In the past few years we have added additional paths through the computational science program. As this program was growing, several colleagues and I developed a simple, but highly flexible and accurate numerical solver for differential equations. This has led to the development of software that calculates and visualizes trajectories for dynamical systems.  I will present an overview of the computational science program as well as our numerical solver.

Finite Matrix Approximations in Computational Quantum Mechanics
Paul Stanley, Beloit College

We show how the creation and annihilation operators commonly associated with the harmonic oscillator Hamiltonian can be used to numerically find the quantum eigenvalues of other Hamiltonians. We compare the 1-D results to the WKB approximation, and discuss the issues of convergence, implementation, and computation times for symbolic processors such as Maple and Mathematica. We then outline the method for generalizing to higher dimensional systems and the construction of appropriate raising and lowering operators. These techniques provide an arena for the exercising of computational methods on quantum systems that are normally considered inaccessible to undergraduate students.

Computational Methods in Applied Physics at Bethel University
Keith Stein, Bethel University

A major in applied physics was added to the Bethel University curriculum in 2002. This B.S. degree in applied physics is built on a solid physics core with additional emphasis in the use of computers (as modeling and laboratory tools), applied optics, engineering techniques, and chemistry. “Computer Methods in Applied Physics and Engineering” is a course offered as part of this major which emphasizes the use of computers as tools in both numerical modeling and experimental research. Students are taught the basics of Matlab programming to address numerical modeling aspects of the course and LabVIEW for the experimental aspects. Student skills and experiences using Matlab and LabVIEW are applied and enhanced through advanced lab projects of upper level physics courses and in undergraduate student research. Examples will be presented on how the emphasis on computer methods has served to enhance undergraduate student research at Bethel University.

Computational Physics at Berry College, In and Out of the Classroom
Todd Timberlake, Berry College

The Berry College physics program has only 3 faculty, and of those I am the only one with significant experience in computational physics. As a result the responsibility of integrating computation into the physics curriculum has fallen largely on my shoulders. I have introduced students to computational physics in two main ways: through computational assignments in my two-semester classical mechanics sequence, and through student involvement in undergraduate research. In both of the classical mechanics courses all students are required to complete several major computational assignments using Mathematica. In the second-semester course students are additionally required to write formal papers (typeset using Mathematica or LaTeX, and incorporating figures, etc.) describing their work and the results. Student use of computation in undergraduate research has ranged from the use of Mathematica to study simple quantum systems to the creation of sophisticated FORTRAN and Java programs to conduct original research in quantum chaos. [Poster PDF]  [Website]

Integrating Computation into the Curriculum with Applications to Nonlinear Dynamics
Brian Utter, James Madison University

The James Madison University Department of Physics and Astronomy is currently in the process of increasing the computational component in our physics major. Currently, students take a required course ‘Computers and Numerical Algorithms’ through the math department with a few continuing in a computational fluid mechanics class. Recently, greater emphasis has been placed in the introductory sequence on introducing basic computation through Excel, Matlab, and Maple. We are also supplementing the advanced curriculum by integrating computation into advanced courses where appropriate and offering a physics-specific computation course that builds on the required math course. I will specifically present plans for the computation course this fall and applications to be covered in an advanced course on nonlinear dynamics and chaos in the following spring, in addition to the hurdles we’ve encountered in general while integrating computational methods into the curriculum.

Computer Simulations - An Introduction to Scientific Research
Katharina Vollmayr-Lee, Bucknell University

I will present a computer simulation course for seniors which I have taught both as an interdisciplinary course and as a physics course. In this course students are exposed to topics such as the Game of Life, traffic flow, fractal growth, population dynamics, random walks, nonlinear dynamics of the driven damped pendulum, the dynamics of many particle systems, and the Ising model. The course is mainly lab based. (For more details see capstone courses on the web page The course introduces the students to scientific research via individual semester long projects. For these projects each student does a literature search, writes a program, analyzes data, and presents the data in the form of a paper and a talk. I will comment on both successes and difficulties with the courses.

Computational Quantum Mechanics
J Jay Wang, University of Massachusetts Dartmouth

We describe a component in a computational physics course dealing with simulations of quantum mechanical systems. The goal was to increase the effective understanding of quantum mechanics by making it visual and more intuitive. We found the coupled-channel method commonly used in atomic/optical physics calculations to be useful. In this method, the Schroedinger equation is expanded in a basis set, reducing it to a set of ordinary differential equations. The advantages of the method are that it can be directly applied to many time-dependent problems, and it can use higher order numerical solutions to ODEs typically developed fairly early in a computational physics course. As an example, we will present numerical Rabi flopping which illustrates several ideas, including resonant and non-resonant transitions, perturbative and strong interactions, and the applicability of two-state and rotating wave approximations. [Poster PDF]

Integrating Undergraduate Research into the Computational Curriculum
Jie Zou, Eastern Illinois University

Undergraduate research is an integral part of the curriculum for the new option, B.S. in Computational Physics, at Eastern Illinois University. One area that I have introduced to our students is computational methods for modeling properties of nanoscale materials, an interdisciplinary field of both scientific and technological significance. The specific projects students have participated in include modeling of thermal conductivity in semiconductor nanoscale films and heterostructures. One of the problems that students have tackled is to obtain phonon dispersions by solving the lattice wave equation using the finite-difference method. The goal of the projects is to not only strengthen students’ understanding of the physics concepts involved, but also equip them with the skills necessary for their future career through a first-hand experience in computation. In this poster, I will provide a summary of the above projects, with a particular focus on the benefits they have brought to our undergraduate students.