Chandralekha Singh

Student understanding of quantum mechanics

We investigate the difficulties of advanced undergraduate students toward the end of a full year upper-level quantum mechanics course with concepts related to quantum measurements and time development. Our analysis is based upon a test administered to 89 students from six universities and interviews with 9 students. Strikingly, most students shared the same difficulties despite variations in background, teaching styles, and textbooks. Concepts related to stationary states, eigenstates, and time dependence of expectation values were found to be particularly difficult. An analysis of written tests and interviews suggests that widespread misconceptions originate from an inability to discriminate between related concepts and a tendency to overgeneralize.

Multiple-choice test of energy and momentum concepts

We investigate student understanding of energy and momentum concepts at the level of introductory physics by designing and administering a 25-item multiple choice test and conducting individual interviews. We find that most students have difficulty in qualitatively interpreting basic principles related to energy and momentum and in applying them in physical situations.

When physical intuition fails

We analyze the problem-solving strategies of physics professors in a case where their physical intuition fails. A nonintuitive introductory-level problem was identified and posed to twenty physics professors. The problem placed the professors in a situation often encountered by students, and their response highlights the importance of intuition and experience in problem solving. Although professors had difficulty in solving the problem under the time constraint, they initially employed a systematic approach, for example, visualizing the problem, considering various conservation laws, and examining limiting cases. After finding that familiar techniques were not fruitful, they made incorrect predictions based on one of two equally important factors. In contrast, other more familiar problems that require the consideration of two important principles (for example, conservation of both energy and momentum for a ballistic pendulum) were quickly solved by the same professors. The responses of students who were given the same problem reflected no overarching strategies or systematic approaches, and a much wider variety of incorrect responses were given. This investigation highlights the importance of teaching effective problem-solving heuristics, and suggests that instructors assess the difficulty of a problem from the perspective of beginning students.

Improving students’ understanding of quantum mechanics

To address the misconceptions that students typically hold concerning quantum mechanics, instructors should couple computer-based visualizations with research-based pedagogical strategies.

Interactive learning tutorials on quantum mechanics

We discuss the development and evaluation of quantum interactive learning tutorials (QuILTs), which are suitable for undergraduate courses in quantum mechanics. QuILTs are based on the investigation of student difficulties in learning quantum physics. They exploit computer-based visualization tools and help students build links between the formal and conceptual aspects of quantum physics without compromising the technical content. They can be used both as supplements to lectures or as self-study tools.

Student understanding of quantum mechanics at the beginning of graduate instruction

A survey was developed to probe student understanding of quantum mechanics at the beginning of graduate instruction. The survey was administered to 202 physics graduate students enrolled in first-year quantum mechanics courses from seven universities at the beginning of the first semester. We also conducted one-on-one interviews with fifteen graduate or advanced undergraduate students who had just completed a course in which all the content on the survey was covered. Although students from some universities performed better on average than others, we found that students share universal difficulties understanding the concepts of quantum mechanics. The difficulties were often due to overgeneralizations of concepts learned in one context to other contexts where they are not directly applicable. Difficulties in distinguishing between closely related concepts and making sense of the formalism of quantum mechanics were common. The results of this study can sensitize instructors of first-year graduate quantum ph...

Student understanding of symmetry and Gauss's law of electricity

We investigate the difficulties that students in calculus-based introductory physics courses have with the concepts of symmetry, electric field, and electric flux which are important for applying Gauss’s law. The determination of the electric field using Gauss’s law requires determining the symmetry of a particular charge distribution and predicting the direction of the electric field everywhere if a high symmetry exists. Effective application of Gauss’s law implicitly requires understanding the principle of superposition for electric fields. Helping students learn when Gauss’s law can be readily applied to determine the strength of the electric field, and then helping them learn to determine the appropriate shape of Gaussian surfaces if sufficient symmetry exists, can help develop their reasoning and problem-solving skills. We administered free-response and multiple-choice questions and conducted interviews with individual students using a think-aloud protocol to elucidate the difficulties that students ...

Theory of polymer chains tethered at interfaces

Abstract Using self-consistent field calculations and scaling analysis, we determined the property of polymers that are tethered onto impenetrable, solid surfaces or adsorbed onto penetrable interfaces. In the case of impenetrable solids, we consider homogeneous walls, as well as surfaces containing chemically distinct patterns. These findings provide guidelines for tailoring the morphology of the polymer layer and thereby controling the interaction between polymer-coated surfaces. In particular, we pinpoint routes for creating ordered arrays of polymer-coated colloidal particles. The results also yield prescriptions for creating laterally patterned polymer films, which are useful in device applications. In the case of penetrable interfaces, we examine the adsorption of polymers into layers of tethered chains. These studies yield design criteria for creating selective filtration and separation systems, and insight into how adsorbing chains interact with a soft, responsive surface.

Student understanding of rotational and rolling motion concepts

We investigated the common difficulties that students have with concepts related to rotational and rolling motion covered in the introductory physics courses. We compared the performance of calculus- and algebra-based introductory physics students with physics juniors who had learned rotational and rolling motion concepts in an intermediate level mechanics course. Interviews were conducted with six physics juniors and ten introductory students using demonstration-based tasks. We also administered free-response and multiple-choice questions to a large number of students enrolled in introductory physics courses, and interviewed six additional introductory students on the test questions (during the test design phase). All students showed similar difficulties regardless of their background, and higher mathematical sophistication did not seem to help acquire a deeper understanding. We found that some difficulties were due to related difficulties with linear motion, while others were tied specifically to the more intricate nature of rotational and rolling motion.

Surveying students’ understanding of quantum mechanics in one spatial dimension

We explore the difficulties that advanced undergraduate and graduate students have with non-relativistic quantum mechanics of a single particle in one spatial dimension. To investigate these difficulties we developed a conceptual survey and administered it to more than 200 students at 10 institutions. The issues targeted in the survey include the set of possible wavefunctions, bound and scattering states, quantum measurement, expectation values, the role of the Hamiltonian, and the time-dependence of the wavefunction and expectation values. We find that undergraduate and graduate students have many common difficulties with these concepts and that research-based tutorials and peer-instruction tools can significantly reduce these difficulties. The findings also suggest that graduate quantum mechanics courses may not be effective at helping students to develop a better conceptual understanding of these topics, partly because such courses mainly focus on quantitative assessments.