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Full-Text Articles in Physical Sciences and Mathematics
Lambert W Function Methods In Double Square Well And Waveguide Problems, Narola Harsh Bharatbhai, P C Deshmukh, Robert B. Scott, Ken Roberts, Sree Ram Valluri
Lambert W Function Methods In Double Square Well And Waveguide Problems, Narola Harsh Bharatbhai, P C Deshmukh, Robert B. Scott, Ken Roberts, Sree Ram Valluri
Physics and Astronomy Publications
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 …
Tutorial: The Quantum Finite Square Well And The Lambert W Function, Sree Ram Valluri, Ken Roberts
Tutorial: The Quantum Finite Square Well And The Lambert W Function, Sree Ram Valluri, Ken Roberts
Physics and Astronomy Publications
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 …