Employing an operator form of the Rodrigues formula to calculate wavefunctions without differential equations

The factorization method of Schrodinger shows us how to determine the energy eigenstates without needing to determine the wavefunctions in position or momentum space. A strategy to convert the energy eigenstates to wavefunctions is well known for the one-dimensional simple harmonic oscillator by employing the Rodrigues formula for the Hermite polynomials in position or momentum space. In this work, we illustrate how to generalize this approach in a representation-independent fashion to find the wavefunctions of other problems in quantum mechanics that can be solved by the factorization method. We examine three problems in detail: (i) the one-dimensional simple harmonic oscillator; (ii) the three-dimensional isotropic harmonic oscillator; and (iii) the three-dimensional Coulomb problem. This approach can be used in either undergraduate or graduate classes in quantum mechanics.Comment: (10 pages, 1 figure, plus supplemental material

Role of Bipolaron Mechanism and Electron-hole Pair Formation in Organic Magnetoresistance

Color poster with text, models, and images.As a magnetic field is introduced into the region of the organic device, the amount of current flowing through the organic layer changes, indicating a change in the material's conductance. In this research project, a mathematical model was created to describe this phenomenon.University of Wisconsin--Eau Claire Office of Research and Sponsored Program

Design and Equipment Considerations for Organic Light Emitting Diodes Experiments

Color poster with text, images, graphs, and models.The purpose of this study is to examine organic light emitting diodes (OLEDs) for new purposes in the optical technology field.University of Wisconsin--Eau Claire Office of Research and Sponsored Programs