Physics and Astronomy Publications
Document Type
Article
Publication Date
2020
Journal
Journal of Physics Communications
Volume
4
First Page
1
Last Page
21
URL with Digital Object Identifier
https://doi.org/10.1088/2399-6528/ab92d9
Abstract
Using methods related to the Lambert W function, we present solutions of two apparently different problems: (1) The one-dimensional double square well potential in quantum mechanics and (2) The transverse electric and magnetic modes for a step-index electromagnetic waveguide. The solution techniques provide insight into the bound energy states for the single and double square well problems and the allowed modes of propagation in a waveguide with varying refractive indices. The solutions can be viewed in either of two related complex plane representations. Comparison of the solution geometries suggests that interesting applications may be possible in nanostructures and devices which are designed to be sensitive to small changes in their environment.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Notes
This article was originally published in Journal of Physics Communications and is available at https://doi.org/10.1088/2399-6528/ab92d9