2016/11/17 by Ken Roberts, S.R. Valluri
Engineering · Physics and Astronomy · #Experimental and Theoretical Physics Studies #Mechanics and Biomechanics Studies #Sports Dynamics and Biomechanics
paper · doi:10.1139/cjp-2016-0602
openalex created_date 2016/06/24 · openalex publication_date 2016/11/17 · crossref created 2016/11/17 · crossref issued 2017/02/01 · crossref published 2017/02/01 · crossref published-print 2017/02/01 · crossref deposited 2025/07/02 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/30
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.