New Quantum Exchange collection resources
http://www.compadre.org/quantum/
The latest material additions to the Quantum Exchange.en-USCopyright 2017, ComPADRE.orgeditor@thequantumexchange.orgeditor@thequantumexchange.orgFri, 23 Jun 2017 17:12:02 ESThttp://blogs.law.harvard.edu/tech/rsshttp://www.compadre.org/portal/services/images/LogoSmallQuantum.gifQuantum Exchange
http://www.compadre.org/quantum/
12535QuVis: Symmetric Perturbation
http://www.compadre.org/quantum/items/detail.cfm?ID=14399
This program illustrates the quantum states of a one-dimensional infinite square well with a symmetric constant-energy step perturbation. The perturbed eigenfunctions are calculated, both ground and several excited states, as well as the expansion coefficients in terms of the unperturbed eigenfunctions. A challenge section asks the user to answer various questions regarding mixing coefficients and the results of the perturbation.
This simulation is part of a collection of animations/simulations for the teaching of concepts in quantum mechanics.Quantum Physics/Approximation Techniques/Rayleigh-Schrodinger Perturbation Theoryhttp://www.compadre.org/quantum/bulletinboard/Thread.cfm?ID=14399Fri, 23 Jun 2017 17:12:02 ESThttp://www.compadre.org/quantum/items/detail.cfm?ID=14399Addressing Student Models of Energy Loss in Quantum Tunneling
http://www.compadre.org/quantum/items/detail.cfm?ID=12083
We report on a multi-year, multi-institution study to investigate students' reasoning about energy in the context of quantum tunneling. We use ungraded surveys, graded examination questions, individual clinical interviews and multiple-choice exams to build a picture of the types of responses that students typically give. We find that two descriptions of tunneling through a square barrier are particularly common. Students often state that tunneling particles lose energy while tunneling. When sketching wavefunctions, students also show a shift in the axis of oscillation, as if the height of the axis of oscillation indicated the energy of the particle. We find inconsistencies between students' conceptual, mathematical and graphical models of quantum tunneling. As part of a curriculum in quantum physics, we have developed instructional materials designed to help students develop a more robust and less inconsistent picture of tunneling, and present data suggesting that we have succeeded in doing so.
Quantum Physics/Probability, Waves, and Interferencehttp://www.compadre.org/quantum/bulletinboard/Thread.cfm?ID=12083Tue, 20 Jun 2017 16:58:42 ESThttp://www.compadre.org/quantum/items/detail.cfm?ID=12083Tutorials on thinking about quantum entities
http://www.compadre.org/quantum/items/detail.cfm?ID=14317
This web site provides a series of tutorials developed to support students in transforming their ontological conceptions about quantum phenomena: their sense of whether something is a particle, a wave, or some other kind of thing, and to make students more aware of their own thinking about these issues. These tutorials are not designed to introduce new content, but can be used alongside other course materials. Each 1-hour tutorial is done with groups of 3-5 students discussing the questions. They are not intended for the answers to be handed in, and in many cases there is not a single “correct” answer.
These tutorials were first designed to be used in a modern physics course for engineering students. Testing has shown they are useful for physics majors. Topics range from plane waves and particle-in-a-box models to the Zeeman Effect and LEDs.
Instructors are welcome to adapt these tutorials. Instructor guides are available for each tutorial that provide information about the intent of the tutorials and some of the results from their use.Quantum Physics/Generalhttp://www.compadre.org/quantum/bulletinboard/Thread.cfm?ID=14317Wed, 08 Feb 2017 17:59:28 ESThttp://www.compadre.org/quantum/items/detail.cfm?ID=14317PICUP
http://www.compadre.org/quantum/items/detail.cfm?ID=14183
The Partnership for Integrating Computation into Undergraduate Physics, or PICUP, is an organization dedicated to the integration of computational physics in undergraduate education. This web site is a community site for sharing computational exercises and pedagogy. The materials provided include computational exercises, example code, background information, and instructor's guides.General Physics/Computational Physicshttp://www.compadre.org/quantum/bulletinboard/Thread.cfm?ID=14183Sat, 31 Dec 2016 12:33:21 ESThttp://www.compadre.org/quantum/items/detail.cfm?ID=14183Student Understanding of Superposition: Vectors and Wave Functions
http://www.compadre.org/quantum/items/detail.cfm?ID=14208
As part of a broad investigation of student understanding in physics, we have examined student ability with superposition throughout introductory and upper-division courses in physics. This research has focused on examining student ability to add and subtract vector quantities and the wave functions associated with quantum physics. We present results from a series of research tasks designed to probe student understanding of superposition in each of these contexts at various points in undergraduate instruction. In addition, we describe and discuss certain patterns in student reasoning that have been identified across the different tasks, contexts, and courses.Quantum Physics/Foundations and Measurements/Probability and Interferencehttp://www.compadre.org/quantum/bulletinboard/Thread.cfm?ID=14208Sat, 31 Dec 2016 12:29:40 ESThttp://www.compadre.org/quantum/items/detail.cfm?ID=14208Developing and evaluating an interactive tutorial on degenerate perturbation theory
http://www.compadre.org/quantum/items/detail.cfm?ID=14225
We discuss an investigation of student difficulties with degenerate perturbation theory (DPT) carried out in advanced quantum mechanics courses by administering free-response and multiple-choice questions and conducting individual interviews with students. We find that students share many common difficulties related to this topic. We used the difficulties found via research as resources to develop and evaluate a Quantum Interactive Learning Tutorial (QuILT) which strives to help students develop a functional understanding of DPT. We discuss the development of the DPT QuILT and its preliminary evaluation in the undergraduate and graduate courses.Quantum Physics/Approximation Techniques/Rayleigh-Schrodinger Perturbation Theoryhttp://www.compadre.org/quantum/bulletinboard/Thread.cfm?ID=14225Sat, 31 Dec 2016 11:51:36 ESThttp://www.compadre.org/quantum/items/detail.cfm?ID=14225Energy measurement resources in spins-first and position-first quantum mechanics
http://www.compadre.org/quantum/items/detail.cfm?ID=14237
Research into student understanding of quantum mechanics has primarily focused on the identification of student difficulties and the development of curriculum that can help improve student learning. Most of this work has been performed in courses using a position-first instructional paradigm. Recently, there has been increase in the number of instructors choosing to present material in an alternate order: spins-first. In this work, we makes steps towards answering the question of whether or not the instructional paradigm has an impact on student thinking about energy measurement. We use a resources lens to analyze the different tools and methods students are using to solve questions.Quantum Physics/Spin and Finite Dimensional Systemshttp://www.compadre.org/quantum/bulletinboard/Thread.cfm?ID=14237Sat, 31 Dec 2016 11:40:25 ESThttp://www.compadre.org/quantum/items/detail.cfm?ID=14237Student Understanding of Period in Introductory and Quantum Physics Courses
http://www.compadre.org/quantum/items/detail.cfm?ID=14274
Time dependence is an important concept in quantum mechanics that has been shown to be difficult for many students. In trying to understand the problems that students encounter, the Physics Education Group at the University of Washington is examining student ability to reason about the period of quantum states. As part of this investigation, we have begun to probe student understanding of period in other contexts (<em>e.g.</em>, phasors and circular motion). Results from analogous written tasks administered in introductory and sophomore-level courses reveal related difficulties. The findings have implications for instruction and are guiding the design of curriculum (<em>Tutorials in Physics: Quantum Mechanics</em>) that is intended to improve student understanding of time dependence in quantum mechanics.Quantum Physics/Foundations and Measurements/Time Dependencehttp://www.compadre.org/quantum/bulletinboard/Thread.cfm?ID=14274Sat, 31 Dec 2016 10:59:36 ESThttp://www.compadre.org/quantum/items/detail.cfm?ID=14274Student understanding of potential, wavefunctions and the Jacobian in hydrogen in graduate-level quantum mechanics
http://www.compadre.org/quantum/items/detail.cfm?ID=14239
This study examined student difficulties related to the potential in the hydrogen atom, and the corresponding ground state, with special attention paid to the role of the Jacobian. The study focused on a population of graduate students at The Ohio State University, and their ability to (1) sketch the approximate potential and radial part of the ground state wavefunction in hydrogen, and (2) their ability to relate this prerequisite knowledge to another relevant quantity: the Bohr radius. Student responses to a sequence of three questions were obtained at the beginning and end of the students’ final semester of graduate quantum mechanics. Several prevalent difficulties were identified that persisted to the end of the course, including an inability to sketch the above-mentioned basic features of hydrogen, and a lack of understanding of the Bohr radius.Quantum Physics/Bound State Systems/Hydrogen Atomhttp://www.compadre.org/quantum/bulletinboard/Thread.cfm?ID=14239Fri, 30 Dec 2016 00:36:46 ESThttp://www.compadre.org/quantum/items/detail.cfm?ID=14239Student difficulties with determining expectation values in quantum mechanics
http://www.compadre.org/quantum/items/detail.cfm?ID=14259
The expectation value of an observable is an important concept in quantum mechanics. However, upper-level undergraduate and graduate students in physics have both conceptual and procedural difficulties when determining the expectation value of physical observables, especially when using Dirac notation. To investigate these difficulties, we administered free-response and multiple-choice questions and conducted individual interviews with students. Here, we discuss the analysis of data on student difficulties when determining the expectation value.Quantum Physics/Foundations and Measurements/Projection Operatorshttp://www.compadre.org/quantum/bulletinboard/Thread.cfm?ID=14259Fri, 30 Dec 2016 00:29:07 ESThttp://www.compadre.org/quantum/items/detail.cfm?ID=14259Student difficulties with representations of quantum operators corresponding to observables
http://www.compadre.org/quantum/items/detail.cfm?ID=14232
Dirac notation is used commonly in quantum mechanics. However, many upper-level undergraduate and graduate students in physics have difficulties with representations of quantum operators corresponding to observables especially when using Dirac notation. To investigate these difficulties, we administered free-response and multiple-choice questions and conducted individual interviews with students in advanced quantum mechanics courses. We discuss the analysis of data on the common difficulties found.Quantum Physics/Foundations and Measurements/Hilbert Spacehttp://www.compadre.org/quantum/bulletinboard/Thread.cfm?ID=14232Fri, 30 Dec 2016 00:22:18 ESThttp://www.compadre.org/quantum/items/detail.cfm?ID=14232Double Slit Wave-Particle JS Model
http://www.compadre.org/quantum/items/detail.cfm?ID=13753
The Double Slit Wave-Particle JavaScript Model demonstrates how matter and light display both wave- and particle-like properties in single and double slit experiments. The simulation shows a detector screen placed behind an aperture with one or two open slits. Particles (electrons or photons) pass through the experiment one at a time and their impact is recorded on the screen. Although it is at first difficult to discern a pattern, a diffraction (interference) pattern eventually emerges suggesting that each particle is interfering with itself. The particle seems to be going through both slits as if it were a wave but is detected (observed) at only one location as if were a particle. In other words, each particle is interfering with itself as if it were simultaneously passing through both slits.
The Double Slit Wave-Particle Duality JavaScript Model was developed using the Easy Java/JavaScript Simulations (EjsS) modeling tool. You can examine and modify this simulation if you have EjsS version 5.2 or above installed by importing the model's zip archive into EjsS.Quantum Physics/Probability, Waves, and Interferencehttp://www.compadre.org/quantum/bulletinboard/Thread.cfm?ID=13753Sat, 19 Nov 2016 09:00:38 ESThttp://www.compadre.org/quantum/items/detail.cfm?ID=13753Making Quantum Mechanics Visual and Interactive
http://www.compadre.org/quantum/items/detail.cfm?ID=13971
This presentation describes class-tested curricular material that use interactive Open Source Physics (OSP) based curricular material in support the teaching of quantum mechanics. The material addresses both quantitative and conceptual difficulties encountered by many students in such topics as wave function shape, momentum space, time evolution, and classical/quantum correlations.Quantum Physics/Generalhttp://www.compadre.org/quantum/bulletinboard/Thread.cfm?ID=13971Sat, 19 Nov 2016 07:19:04 ESThttp://www.compadre.org/quantum/items/detail.cfm?ID=13971Institute of Physics Quantum Physics Resources
http://www.compadre.org/quantum/items/detail.cfm?ID=13070
Quantum theory has a reputation for being difficult to grasp and removed from real-world problems. This free educational resource from the UK Institute of Physics challenges this stereotype by offering a new quantum curriculum to support undergraduate physics students and instructors.
Unlike traditional approaches based on continuum wave mechanics, this approach immediately immerses students in inherently quantum mechanical concepts by focusing on experiments that have no classical explanation. Specifically, it is built around discrete two-level systems such as spin-1/2 particles, interferometers and qubits. This allows, from the start, a discussion of the interpretive aspects of quantum mechanics and its modern applications in quantum information processing without the need to first cover integrals and differential equations.
The site allows users to approach quantum theory from these and more traditional perspectives by organizing the core content across five distinct themes. In addition to over 80 commissioned articles, the site offers numerous interactive simulations, problem sets and a glossary of terms. A sliding scale at the base of each article allows users to tag their level of understanding. This information is stored and displayed in the navigation panel for users to track their progress.
Solutions to activities and problems and a complete download of all content on the site are available to instructors by emailing quantumphysics@iop.org. Instructors can also request to modify materials.Quantum Physics/Generalhttp://www.compadre.org/quantum/bulletinboard/Thread.cfm?ID=13070Tue, 21 Jun 2016 15:04:34 ESThttp://www.compadre.org/quantum/items/detail.cfm?ID=13070Werner Heisenberg
http://www.compadre.org/quantum/items/detail.cfm?ID=1271
This web page provides a biography of Werner Heisenberg. It is part of an extensive collection of biographies of mathematicians from the University of St. Andrews.General Physics/Historyhttp://www.compadre.org/quantum/bulletinboard/Thread.cfm?ID=1271Tue, 21 Jun 2016 14:54:57 ESThttp://www.compadre.org/quantum/items/detail.cfm?ID=1271Dirac Delta Scattering Model
http://www.compadre.org/quantum/items/detail.cfm?ID=6990
The Ejs Dirac Delta Scattering model displays the time evolution of a plane wave incident on a Dirac delta function barrier. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_DiracDeltaScattering.jar file will run the program if Java is installed. The default wave function shows a right-moving plane wave incident on the barrier. The energy of the wave function can be changed with the slider. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting “Open Ejs Model” from the pop-up menu item.
Ejs Dirac Delta Scattering model was created using the Easy Java Simulations (Ejs) modeling tool. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Open Source Physics programs for quantum mechanics are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs.Quantum Physics/Scattering and Continuum State Systemshttp://www.compadre.org/quantum/bulletinboard/Thread.cfm?ID=6990Tue, 21 Jun 2016 14:52:28 ESThttp://www.compadre.org/quantum/items/detail.cfm?ID=6990Quilt JS Package: Time Evolution of a Wave Function
http://www.compadre.org/quantum/items/detail.cfm?ID=13737
The QuILT JavaScript package contains exercises for the teaching of time evolution of wave functions in quantum mechanics. The file contains ready-to-run JavaScript simulations and a set of curricular materials. The material presents a computer-based tutorial on the “Time Evolution of the Wave Function.” This package is one of the recently developed computer-based tutorials that have resulted from the collaboration of the Quantum Interactive Learning Tutorials (QuILT) project and the Open Source Physics (OSP) project.
Other Java and JavaScript packages for teaching Quantum Mechanics are also available. They can be found by searching ComPADRE for QuILT or Quantum Mechanics.Quantum Physics/Bound State Systemshttp://www.compadre.org/quantum/bulletinboard/Thread.cfm?ID=13737Tue, 21 Jun 2016 11:39:04 ESThttp://www.compadre.org/quantum/items/detail.cfm?ID=13737Student difficulties with quantum states while translating state vectors in Dirac notation to wave functions in position and momentum representations
http://www.compadre.org/quantum/items/detail.cfm?ID=13873
Dirac notation is often used in upper level quantum mechanics courses, but students struggle with this representation. To investigate the difficulties that advanced students (i.e., upper-level undergraduate and graduate students) have while translating state vectors in Dirac notation to wave functions in position and momentum representations, we administered free-response and multiple-choice questions and conducted individual interviews with students. We find that students display common difficulties with these topics.Quantum Physics/Foundations and Measurements/Hilbert Spacehttp://www.compadre.org/quantum/bulletinboard/Thread.cfm?ID=13873Wed, 23 Dec 2015 19:40:09 ESThttp://www.compadre.org/quantum/items/detail.cfm?ID=13873Developing and evaluating a tutorial on the double-slit experiment
http://www.compadre.org/quantum/items/detail.cfm?ID=13893
Learning quantum mechanics is challenging, even for upper-level undergraduate and graduate students. Interactive tutorials which build on students’ prior knowledge can be useful tools to enhance student learning. We have been investigating student difficulties with the quantum mechanics pertaining to the double-slit experiment in various situations. Here we discuss the development and evaluation of a Quantum Interactive Learning Tutorial (QuILT) which makes use of an interactive simulation to improve student understanding. We summarize common difficulties and discuss the extent to which the QuILT is effective in addressing them in two types of courses.Quantum Physics/Probability, Waves, and Interferencehttp://www.compadre.org/quantum/bulletinboard/Thread.cfm?ID=13893Wed, 23 Dec 2015 19:24:41 ESThttp://www.compadre.org/quantum/items/detail.cfm?ID=13893Investigating Student Understanding of Perturbation Theory and the Inner Products of Functions
http://www.compadre.org/quantum/items/detail.cfm?ID=13883
We have investigated the extent to which students can qualitatively determine the effect of perturbations to a Hamiltonian on the energies of the eigenfunctions. The results indicate that after lecture instruction many students cannot determine some important features of the first-order correction. We examine the possibility that this failure may stem from a lack of understanding of the inner product. Since perturbations are often represented graphically, the focus has been on student ability to determine the inner product of functions represented graphically. In the process, we have found that some students are unable to find inner products even in contexts outside of quantum mechanics.Quantum Physics/Foundations and Measurements/Hilbert Spacehttp://www.compadre.org/quantum/bulletinboard/Thread.cfm?ID=13883Wed, 23 Dec 2015 17:16:06 ESThttp://www.compadre.org/quantum/items/detail.cfm?ID=13883