Teaching the noncommutativity of the product of matrices to high school or college level students is a difficult task when approached from a purely formal perspective. The aim of this paper is to present a simple experimental activity for teaching the noncommutativity of the matrix product, based on the Jones calculus, a mathematical formalism for…

This article utilizes a framework for classifying different scientific methods suggested by a philosopher of science (Brandon "Synthese," 99, 59-73, 1994) called Brandon's Matrix. It presents findings from teachers who took part in a funded project in England that looked at the nature of scientific methods in science investigations.…

Contemporary science education themes are marked by the inevitable uncertainty of consequences emerging from human actions. They encompass disasters, pandemics and other events that have been marking our present times. Understanding new risks as the ones resulting from human action, even when proposing a solution for an issue, is one of the…

Undergraduate quantum mechanics (QM) uses a variety of notations, each with their own advantages and constraints, for representing quantum states and carrying out individual calculations. An example of this can be seen when calculating expectation values, which can be solved using several different methods. Analysis of written exam data given at…

Slater type orbitals were used to construct the overlap and the Hamiltonian core matrices; we also found the values of the bi-electron repulsion integrals. The Hartree Fock Roothaan approximation process starts with setting an initial guess value for the elements of the density matrix; with these matrices we constructed the initial Fock matrix.…

Decision matrices are valuable engineering tools. They allow engineers to objectively examine solution options. Decision matrices can be incorporated in K-12 classrooms to support authentic engineering instruction. In this article we provide examples of how decision matrices have been incorporated into 6th and 7th grade classrooms as part of an…

The formalism of quantum mechanics includes a rich collection of representations for describing quantum systems, including functions, graphs, matrices, histograms of probabilities, and Dirac notation. The varied features of these representations affect how computations are performed. For example, identifying probabilities of measurement outcomes…

Matrix diagonalization, the key technique at the heart of modern computational chemistry for the numerical solution of the Schrödinger equation, can be easily introduced in the physical chemistry curriculum in a pedagogical context using simple Hückel molecular orbital theory for p bonding in molecules. We present details and results of…

Data were gathered from 95 Year 10 students in a New Zealand secondary school to explore how the indicators of scientific literacy are expressed in student responses. These students completed an activity based around the two contexts of lighting and health. A matrix, which incorporated descriptive indicators, was developed to analyse the student…

The Lindblad equation is an evolution equation for the density matrix in quantum theory. It is the general linear, Markovian, form which ensures that the density matrix is Hermitian, trace 1, positive and completely positive. Some elementary examples of the Lindblad equation are given. The derivation of the Lindblad equation presented here is…

The rotational dynamics was studied from the point of view of Rodrigues' vector. This vector is defined here by its connection with other forms of parametrization of the rotation matrix. The rotation matrix was expressed in terms of this vector. The angular velocity was computed using the components of Rodrigues' vector as coordinates. It appears…

A brief history of the development of the empirical equation that is used by prominent, Internet-based programs to estimate (or calculate) the extinction coefficients of proteins is presented. In addition, an overview of a series of related assignments designed to help students understand the origin of the empirical equation is provided. The…

Glass beads are placed in the compartments of a horizontal square grid. This grid is then vertically shaken. According to the reduced acceleration [image omitted] of the system, the granular material exhibits various behaviours. By counting the number of beads in each compartment after shaking, it is possible to define three regimes. At low…

We examine a generalization of the one-dimensional Ising model involving interactions among neighbourhoods of "k" adjacent spins. The model is solved by exploiting a connection to an interesting computational problem that we call ""k"-SAT on a ring", and is shown to be equivalent to the nearest-neighbour Ising model in the absence of an external…

We present an elementary argument showing that the sign of h-bar in the basic formulation of quantum mechanics can be changed without incurring any physical consequences. (Contains 1 footnote.)