New Quantum Exchange collection resources

Improving student understanding of addition of angular momentum in quantum mechanics

Tue, 18 Jun 2013 22:28:14 EST

We describe the difficulties advanced undergraduate and graduate students have with concepts related to addition of angular momentum in quantum mechanics. We also describe the development and implementation of a research-based learning tool, Quantum Interactive Learning Tutorial (QuILT), to reduce these difficulties. The preliminary evaluation shows that the QuILT related to the basics of the addition of angular momentum is helpful in improving students’ understanding of these concepts.

EPR/Bell's Theorem

Tue, 18 Jun 2013 22:23:02 EST

This is a simulation of the simplified EPR-like experiment described by David Mermin's 1981 AJP Article (N. D. Mermin, "Bringing home the atomic world: Quantum mysteries for anybody," Am. J. Phys. 49, 940-943(1981)). The program has internal documentation.

Improving Students' Understanding of Quantum Mechanics

Wed, 20 Feb 2013 18:44:05 EST

Learning physics is challenging at all levels. Students’ difficulties in the introductory level physics courses have been widely studied and many instructional strategies have been developed to help students learn introductory physics. However, research shows that there is a large diversity in students’ preparation and skills in the upper-level physics courses and it is necessary to provide scaffolding support to help students learn advanced physics. This thesis explores issues related to students’ common difficulties in learning upper-level undergraduate quantum mechanics and how these difficulties can be reduced by research-based learning tutorials and peer instruction tools. We investigated students’ difficulties in learning quantum mechanics by administering written tests and surveys to many classes and conducting individual interviews with a subset of students. Based on these investigations, we developed Quantum Interactive Learning Tutorials (QuILTs) and peer instruction tools to help students build a hierarchical knowledge structure of quantum mechanics through a guided approach. Preliminary assessments indicate that students’ understanding of quantum mechanics is improved after using the research-based learning tools in the junior-senior level quantum mechanics courses. We also designed a standardized conceptual survey that can help instructors better probe students’ understanding of quantum mechanics concepts in one spatial dimension. The validity and reliability of this quantum mechanics survey is discussed.

Numerical Solutions to the Schrödinger Equation

Wed, 20 Feb 2013 18:35:09 EST

This Mathematica Notebook provides in introduction to computational methods for studying quantum mechanical systems. Examples given are one dimensional. Studying quantum mechanics in one-dimension allows the student to learn the basics of quantum mechanics and to develop an intuition without some of the mathematical complexities present in three-dimensions.

Improving students’ understanding of quantum measurement. I. Investigation of difficulties

Wed, 20 Feb 2013 18:25:14 EST

We describe the difficulties that advanced undergraduate and graduate students have with quantum measurement within the standard interpretation of quantum mechanics. We explore the possible origins of these difficulties by analyzing student responses to questions from both surveys and interviews. Results from this research are applied to develop research-based learning tutorials to improve students’ understanding of quantum measurement.

Improving students’ understanding of quantum measurement. II. Development of research-based learning tools

Wed, 20 Feb 2013 18:24:35 EST

We describe the development and implementation of research-based learning tools such as the Quantum Interactive Learning Tutorials and peer-instruction tools to reduce students’ common difficulties with issues related to measurement in quantum mechanics. A preliminary evaluation shows that these learning tools are effective in improving students' understanding of concepts related to quantum measurement.

Categorization of quantum mechanics problems by professors and students

Tue, 23 Oct 2012 08:08:19 EST

We discuss the categorization of 20 quantum mechanics problems by physics professors and undergraduate students from two honours-level quantum mechanics courses. Professors and students were asked to categorize the problems based upon similarity of solution. We also had individual discussions with professors who categorized the problems. Faculty members' categorizations were overall rated higher than those of students by three faculty members who evaluated all of the categorizations. The categories created by faculty members were more diverse compared to the categories they created for a set of introductory mechanics problems. Some faculty members noted that the categorization of introductory physics problems often involves identifying fundamental principles relevant for the problem, whereas in upper-level undergraduate quantum mechanics problems, it mainly involves identifying concepts and procedures required to solve the problem. Moreover, physics faculty members who evaluated others' categorizations expressed that the task was very challenging and they sometimes found another person's categorization to be better than their own. They also rated some concrete categories such as 'hydrogen atom' or 'simple harmonic oscillator' higher than other concrete categories such as 'infinite square well' or 'free particle'.

Quantum Mechanics Survey (QMS)

Tue, 23 Oct 2012 08:06:44 EST

This 31-question research-based multiple-choice test is designed to evaluate students’ conceptual understanding of quantum mechanics in junior-level courses. The survey is based on investigations of students’ difficulties in quantum mechanics and should be given in a 50-minute period. Statistical results have shown the survey to be reliable and valid. A summary of the construction and analysis of the survey is available in Surveying students’ understanding of quantum mechanics in one spatial dimension, Am. J. Phys. 80 (3), 252-259. This assessment is free for use by instructors in their classroom. However, as it takes years of development effort to create and validate reliable assessment instruments, the file is password-protected. Furthermore, the author requests that 1. students are not given copies following examination; and 2. none of the questions are incorporated into web-based question delivery systems without adequate security to prevent printing or unauthorized access by students. To obtain the password, please send a request with your name, email, institution, and a link to a page at your institution that confirms you are an instructor.

Improving Students' Understanding of Quantum Mechanics

Tue, 23 Oct 2012 08:04:02 EST

Richard Feynman once famously stated that nobody understands quantum mechanics. He was, of course, referring to the many strange, unintuitive foundational aspects of quantum theory such as its inherent indeterminism and state reduction during measurement according to the Copenhagen interpretation. But despite its underlying fundamental mysteries, the theory has remained a cornerstone of modern physics. Most physicists, as students, are introduced to quantum mechanics in a modern-physics course, take quantum mechanics as advanced undergraduates, and then take it again in their first year of graduate school. One might think that after all this instruction, students would have become certified quantum mechanics, able to solve the Schrödinger equation, manipulate Dirac bras and kets, calculate expectation values, and, most importantly, interpret their results in terms of real or thought experiments. That sort of functional understanding of quantum mechanics is quite distinct from the foundational issues alluded to by Feynman.

Perspectives in Quantum Physics: Epistemological, Ontological and Pedagogical

Tue, 29 May 2012 11:03:07 EST

A common learning goal for modern physics instructors is for students to recognize a difference between the experimental uncertainty of classical physics and the fundamental uncertainty of quantum mechanics. Our studies suggest this notoriously difficult task may be frustrated by the intuitively realist perspectives of introductory students, and a lack of ontological flexibility in their conceptions of light and matter. We have developed a framework for understanding and characterizing student perspectives on the physical interpretation of quantum mechanics, and demonstrate the differential impact on student thinking of the myriad ways instructors approach interpretive themes in their introductory courses. Like expert physicists, students interpret quantum phenomena differently, and these interpretations are significantly influenced by their overall stances on questions central to the so-called measurement problem: Is the wave function physically real, or simply a mathematical tool? Is the collapse of the wave function an ad hoc rule, or a physical transition not described by any equation? Does an electron, being a form of matter, exist as a localized particle at all times? These questions, which are of personal and academic interest to our students, are largely only superficially addressed in our introductory courses, often for fear of opening a Pandora’s Box of student questions, none of which have easy answers. We show how a transformed modern physics curriculum (recently implemented at the University of Colorado) may positively impact student perspectives on indeterminacy and wave-particle duality, by making questions of classical and quantum reality a central theme of our course, but also by making the beliefs of our students, and not just those of scientists, an explicit topic of discussion.

QuVis: Non-interacting Particles in an Infinite Well

Wed, 18 Jan 2012 10:13:12 EST

This animation shows a system of N non-interacting Bose or Fermi particles in an infinitely deep square well. The total involves the distribution of the individual particles across energy levels. Users can choose the type and number of particles in the well and the total energy of the system. This animation includes a step-by-step exploration that explains key points in detail. This animation is part of a collection of animations for the teaching of concepts in quantum mechanics.

Assessing and improving student understanding of quantum mechanics

Fri, 18 Nov 2011 09:38:59 EST

We developed a survey to probe student understanding of quantum mechanics concepts at the beginning of graduate instruction. The survey was administered to 202 graduate students in physics enrolled in first-year quantum mechanics courses from seven different universities at the beginning of the first semester. We also conducted one-on-one interviews with fifteen graduate students or advanced undergraduate students who had just finished a course in which all the content on the survey was covered. We find that students share universal difficulties about fundamental quantum mechanics concepts. The difficulties are often due to over-generalization of concepts learned in one context to other contexts where they are not directly applicable and difficulty in making sense of the abstract quantitative formalism of quantum mechanics. Instructional strategies that focus on improving student understanding of these concepts should take into account these difficulties. The results from this study can sensitize instructors of first-year graduate quantum physics to the conceptual difficulties students are likely to face.

Examining the Evolution of Student Ideas About Quantum Tunneling

Fri, 18 Nov 2011 09:37:08 EST

We have studied whether repeated exposure to complicated physics concepts, such as quantum tunneling, fosters increased understanding. For three students, we have multiple interview, survey, and examination data over three years. We present data from a single student whose understanding of energy conservation in tunneling improved with repeated instruction, but whose ability to correctly sketch wave function solutions and discuss their meaning showed little progress.

Why we should teach the Bohr model and how to teach it effectively

Fri, 18 Nov 2011 06:53:40 EST

Some education researchers have claimed that we should not teach the Bohr model of the atom because it inhibits students’ ability to learn the true quantum nature of electrons in atoms. Although the evidence for this claim is weak, many have accepted it. This claim has implications for how to present atoms in classes ranging from elementary school to graduate school. We present results from a study designed to test this claim by developing a curriculum on models of the atom, including the Bohr and Schrödinger models. We examine student descriptions of atoms on final exams in transformed modern physics classes using various versions of this curriculum. We find that if the curriculum does not include sufficient connections between different models, many students still have a Bohr-like view of atoms rather than a more accurate Schrödinger model. However, with an improved curriculum designed to develop model-building skills and with better integration between different models, it is possible to get most students to describe atoms using the Schrödinger model. In comparing our results with previous research, we find that comparing and contrasting different models is a key feature of a curriculum that helps students move beyond the Bohr model and adopt Schrödinger’s view of the atom. We find that understanding the reasons for the development of models is much more difficult for students than understanding the features of the models. We also present interactive computer simulations designed to help students build models of the atom more effectively.

Quantum Mechanics Conceptual Survey

Fri, 18 Nov 2011 06:52:02 EST

This web page is the home for the Quantum Mechanics Conceptual Survey (QMCS). The goal of this assessment is to provide an accurate measure of students' understanding of fundamental concepts in quantum mechanics. The QMCS is inspired by the many carefully researched and validated tests of conceptual understanding in physics. The authors developed the questions to be independent of notation unique to a specific course and avoiding jargon as much as possible. The questions in the QMCS are based on faculty interviews, textbooks and syllabi, existing assessments, research on student misconceptions in quantum mechanics, and student observations.

Gaussian Wave Packet: Step Scattering

Mon, 01 Aug 2011 10:33:32 EST

The Gaussian Wave Packet: Step Scattering model simulates the time evolution of a free Gaussian wave packet in position space when it is incident on a potential energy step. The position-space wave functions are depicted using three colors on the graph: black which depicts the absolute square of the wave function, blue which depicts the real part of the wave function, and red which depicts the imaginary part of the wave function. The user may change the height of the potential step or the wave packet energy by dragging circles on the energy graph. The initial width of the packet may also be changed. Also shown are the theoretical and calculated transmission and reflection coefficients. The Gaussian Wave Packet: Step Scattering model was created using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_qm_gaussian_step.jar file will run the program if Java is installed.

Active Quantum Mechanics: Tutorials and Writing Assignments

Mon, 01 Aug 2011 10:27:19 EST

This web site contains active-learning tutorials and writing assignments for upper-level undergraduate quantum mechanics. The tutorials focus on the mathematical formalism of quantum mechanics. The writing assignments focus on the interpretation of quantum mechanics, and particularly the role of experiments. The topics cover range from introduction to the Schrodinger equation through perturbation theory. In the course using these materials, students work in small groups to complete worksheet-based tutorials during class time, and do fairly typical homework problems and writing assignments, on their own.

QuVis: The University of St Andrews Quantum Mechanics Visualisation project

Wed, 18 May 2011 23:31:52 EST

This is a collection of animations for the teaching of concepts in quantum mechanics. Each animation includes a step-by-step exploration that explains key points in detail, and most animations include password-protected instructor resources consisting of worksheets with solutions. These animations build on existing education research and the experience of the authors. Each animation specifically targets student misconceptions and areas of difficulty in quantum mechanics. Animations have been used and evaluated in several quantum mechanics courses. The topics covered include bound states in one and two dimensions, scattering states, perturbations, Fermi and Bose statistics, and quantum logic. The development of further animations and extension of site functionality are ongoing.

Solutions Manual for Numerical Solutions to the Schrödinger Equation

Sun, 15 May 2011 00:02:10 EST

This Mathematica notebook contains solutions to several numerical problems and exercises in quantum mechanics. Topics include the shooting method, wavepacket dynamics, probability functions, and the Laplace equation. All of the problems are in one dimension, to help students focus on the physics of quantum systems.

Transfer of Learning in Quantum Mechanics

Sat, 14 May 2011 23:31:07 EST

We investigate the difficulties that undergraduate students in quantum mechanics courses have in transferring learning from previous courses or within the same course from one context to another by administering written tests and conducting individual interviews. Quantum mechanics is abstract and its paradigm is very different from the classical one. A good grasp of the principles of quantum mechanics requires creating and organizing a knowledge structure consistent with the quantum postulates. Previously learned concepts such as the principle of superposition and probability can be useful in quantum mechanics if students are given opportunity to build associations between new and prior knowledge. We also discuss the need for better alignment between quantum mechanics and modern physics courses taken previously because semi-classical models can impede internalization of the quantum paradigm in more advanced courses.