Lambert W function methods in double square well and waveguide problems
| Autor: | Ken Roberts, Narola Harsh Bharatbhai, Sree Ram Valluri, Robert B. Scott, Pranawa C. Deshmukh |
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| Rok vydání: | 2020 |
| Předmět: |
Astrophysics and Astronomy
General Physics and Astronomy 02 engineering and technology 01 natural sciences Square (algebra) Lambert W function law.invention symbols.namesake law 0103 physical sciences Energy level 010306 general physics Quantum well Physics Mathematical analysis waveguides 021001 nanoscience & nanotechnology Transverse plane double square well quantum wells Finite potential well symbols 0210 nano-technology Complex plane Waveguide |
| Zdroj: | Physics and Astronomy Publications |
| ISSN: | 2399-6528 |
| DOI: | 10.1088/2399-6528/ab92d9 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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