Physics and Astronomy Publications
Document Type
Article
Publication Date
2-2017
Journal
CANADIAN JOURNAL OF PHYSICS
Volume
2
Issue
95
First Page
105
Last Page
110
URL with Digital Object Identifier
http://dx.doi.org/10.1139/cjp-2016-0602
Abstract
We present a solution of the quantum mechanics problem of the allowable energy levels of a bound particle in a one-dimensional finite square well. The method is a geometric-analytic technique utilizing the conformal mapping w -> z = we(w) between two complex domains. The solution of the finite square well problem can be seen to be described by the images of simple geometric shapes, lines, and circles, under this map and its inverse image. The technique can also be described using the Lambert W function. One can work in either of the complex domains, thereby obtaining additional insight into the finite square well problem and its bound energy states. This suggests interesting possibilities for the design of materials that are sensitive to minute changes in their environment such as nanostructures and the quantum well infrared photodetector.
Notes
http://dx.doi.org/10.1139/cjp-2016-0602