Open AccessLambert W function methods in double square well and waveguide problems
Author(s) -
Narola Harsh Bharatbhai,
P. C. Deshmukh,
Robert B. Scott,
K. Roberts,
S. R. Valluri
Publication year - 2020
Publication title -
journal of physics communications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.407
H-Index - 17
ISSN - 2399-6528
DOI - 10.1088/2399-6528/ab92d9
Subject(s) - square (algebra) , waveguide , transverse plane , transverse magnetic , lambert w function , function (biology) , physics , refractive index , plane (geometry) , optics , quantum mechanics , mathematical analysis , mathematics , magnetic field , geometry , structural engineering , evolutionary biology , biology , engineering
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.