Lambert W function methods in double square well and waveguide problems

Authors

Narola Harsh Bharatbhai
P C Deshmukh
Robert B. Scott
Ken Roberts
Sree Ram Valluri, University of Western OntarioFollow

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.

Notes

This article was originally published in Journal of Physics Communications and is available at https://doi.org/10.1088/2399-6528/ab92d9

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.