We present noncompetitive adsorption as "particles in a box with one sticky wall." We start with a general model that can be modeled as a simple ordinary differential equation (ODE). To verify the ODE students run a computer simulation. The ODE's solution imperfectly fits the simulation's data. This leads to the diffusion partial…

In a course on chemical applications of symmetry and group theory, students learn to use several useful tools (like character tables, projection operators, and correlation tables), but in the process of learning the mathematical details, they often miss the conceptual big picture about "why" and "how" symmetry leads to the…

An introduction to the Quantum Chemistry Package (QCP), implemented in the computer algebra system Maple, is presented. The QCP combines sophisticated electronic structure methods and Maple's easy-to-use graphical interface to enable computation and visualization of the electronic energies and properties of molecules. Here we describe how the QCP…

Synthesis and characterization of nanomaterials yields opportunities for instruction of related topics in solution chemistry and materials science, as well as spectroscopy connecting to band theory, the "particle in a box" quantum mechanical model, and thermodynamics. In collaboration with an undergraduate research assistant, we have…

At an early stage of learning quantum chemistry, undergraduate students usually encounter the concepts of the particle in a box, the harmonic oscillator, and then the particle on a sphere. Rotational levels of a diatomic molecule can be well approximated by the energy levels of the particle on a sphere. Wave functions for the particle in a…

This manuscript presents an exercise that utilizes mathematical software to explore Fourier transforms in the context of model quantum mechanical systems, thus providing a deeper mathematical understanding of relevant information often introduced and treated as a "black-box" in analytical chemistry courses. The exercise is given to…

Quantum dots (QDs) are useful for demonstrating the particle-in-a-box (PIB) model utilized in quantum chemistry, and can readily be applied to a discussion of both thermodynamics and kinetics in an undergraduate laboratory setting. Modifications of existing synthetic procedures were used to create QDs of different sizes and compositions (CdS…

Many quantum mechanical models are discussed as part of the undergraduate physical chemistry course to help students understand the connection between eigenvalue expressions and spectroscopy. Typical examples covered include the particle in a box, the harmonic oscillator, the rigid rotor, and the hydrogen atom. This article demonstrates that…

It is not often realized by chemists that the special theory of relativity is behind several aspects of quantum chemistry. The Schrdinger equation itself is based on relations between space-time and energy-momentum four vectors. Electron spin is, of course, the most obvious manifestation of relativity. The chemistry of some heavy elements is…

In this experiment, linear polyynes are synthesized and then the predictions of a one-dimensional, particle in a box are used to calculate the quantum mechanical box length for the polyynes. A solution of graphite in ethanol is irradiated with a Nd:YAG laser (532 nm) and the resulting solution is filtered and analyzed. Data from gas…

The Darboux transformation in quantum mechanics is reviewed at a basic level. Examples of how this transformation leads to exactly solvable potentials related to the "particle in a box" and the harmonic oscillator are shown in detail. The connection between the Darboux transformation and some modern operator based approaches to quantum mechanics…

Semiconductor quantum dots are at the forefront of materials science chemistry with applications in biological imaging and photovoltaic technologies. We have developed a simple laboratory experiment to measure the quantum-dot size from fluorescence spectra. A major roadblock of quantum-dot based exercises is the particle synthesis and handling;…

The ready availability of interactive platforms has produced a new generation of students able to utilize computer-based learning tools with ease and comfort. The potential to better "explore by yourself" the lecture material permits students to have an enhanced learning experience and stimulates them to tinker with equation parameters…

The one-dimensional particle-in-a-box model used to introduce quantum mechanics to students suffers from a tenuous connection to a real physical system. This article presents a two-dimensional model, the particle confined within a ring, that directly corresponds to observations of surface electrons in a metal trapped inside a circular barrier.…

We propose an apparatus that emulates the experiment used by Geiger and Marsden in 1913 to investigate alpha particles (Rutherford) scattering. Using a widely available fused deposition modelling 3D-printer, we built a compartmented and easily assembled educational instrument. The whole apparatus is composed of a 3D-printed chamber and an…