We present an algorithm for solving the time-dependent Schrödinger equation that is based on the finite-difference expression of the kinetic energy operator. Students who have some knowledge of linear algebra can understand the theory used to derive the algorithm. This is because the finite-difference kinetic energy matrix and the Hückel matrix…

Work and mechanical energy is a fundamental topic in introductory physics. Studies in existing literature have shown that students have difficulties in understanding work and mechanical energy, particularly the topic of work-energy theorem. To study students' knowledge integration in learning work and mechanical energy, a conceptual framework…

Chemical kinetics is an important topic that is reinforced across the undergraduate chemistry curriculum, but previous research indicates students tend to have difficulty developing a sophisticated understanding of reaction rate. In this qualitative case study, we characterized how two students conceptualized reaction rate in the context of…

In the resolution of problems in chemical kinetics and catalysis the mathematical models relate the independent variable that is usually time, with the dependent variable which is normally the concentration of a reactant. They conform to linear models, whose parameters such as the ordering to origin and the slope are kinetic parameters, applying…

Many introductory physics courses begin with the teaching of motion and kinematics. This naturally leads to the use of constant acceleration equations to solve various problems involving common motions (free fall being a notable example). Students can sometimes get the impression that these equations are the only thing they need to remember in…

The development of good learning resources on inquiry learning model with science literacy as a strategy to facilitate active learning has become a trend in education. Critical thinking ability is needed as a strategy to build students competencies in problem solving and discovery as required in science learning. This study aims to develop a set…

Problem solving is a critical feature of highly quantitative physical science topics, such as chemical kinetics. In order to solve a problem, students must cue into relevant features, ignore irrelevant features, and choose among potential problem-solving approaches. However, what is considered appropriate or productive for problem solving is…

The themes discussed in this study relate to how students reason about the information encoded in rate constants, which is important for developing a deep understanding of chemical kinetics at the molecular level. This study is part of a larger project centered more generally on students' understanding and use of mathematics in chemical kinetics.…

Enzyme kinetics is an essential part of biochemistry programs, which have been gaining importance in recent years for their applications in biotechnology and biomedicine. The teaching and learning of these issues has been traditionally hampered by difficulties that stem mainly from the dynamic and mathematical nature of the topic and the…

Chemical kinetics is a highly quantitative content area that involves the use of multiple mathematical representations to model processes and is a context that is under-investigated in the literature. This qualitative study explored undergraduate student integration of chemistry and mathematics during problem solving in the context of chemical…

As we typically teach in an introductory mechanics course, choosing a "good" coordinate frame with convenient axes may present a major simplification to a problem. Additionally, knowing some conserved quantities provides an extremely powerful problem-solving tool. While the former idea is typically discussed in the context of…

We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data. We estimate the parameters present in several differential equation models of chemical reactions of order n, where n = 0, 1, 2, and apply more general…

Background and purpose: Chemistry examinations can favour the deployment of algorithmic procedures like Le Chatelier's Principle (LCP) rather than reasoning using chemical principles. This study investigated the explanatory resources which high school students use to answer equilibrium problems and whether the marks given for examination answers…

This article describes a comprehensive treatment of experimental enzyme kinetics strongly coupled to electronic data acquisition and use of spreadsheets to organize data and perform linear and nonlinear least-squares analyses, all in a manner that promotes development of important reasoning skills. Kinetic parameters are obtained for the stable…

In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form [psi](r) = u(r)/r, where u(0) [is not equal to] 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly…