1,406 research outputs found

    Siewert solutions of transcendental equations, generalized Lambert functions and physical applications

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    We review the exact solutions of several transcendental equations, obtained by Siewert and his co-workers, in the '70s. Some of them are expressed in terms of the generalized Lambert functions, recently studied by Mez\"o, Baricz and Mugnaini. For some others, precise analytical approximations are obtained. In two cases, the asymptotic form of Siewert's solutions are written as Wright omega functions.Comment: 17 pages, 5 figure

    Waveguides, Resonant Cavities, Optical Fibers and Their Quantum Counterparts

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    Semiconductor Quantum Wells with BenDaniel-Duke Boundary Conditions and Janus Nanorods

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    The energy levels of bound states of an electron in a quantum well with BenDaniel-Duke boundary condition are studied. Analytic, explicit, simple, and accurate formulae have been obtained for the ground state and the first excited state. In our approach, the exact, transcendental eigenvalues equations were replaced with approximate, tractable, algebraic equations, using algebraic approximations for some trigonometric functions. Our method can be applied to both type I and type II semiconductors and easily extended to quantum dots. The same approach was used for the semi-quantitative analyze of two toy models of Janus nanorods

    Quantum Wells and Ultrathin Metallic Films

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    The chapter illustrates how simple quantum mechanics can sometimes provide quite precise description of nanophysics phenomena. From this perspective, both exact and approximate solutions for the bound-state energy of an electron in a square well are exposed. These results are used to improve the calculation of quantum size effects (QSEs) in ultrathin metallic films, obtained by several authors with simpler models of quantum wells. We show that, for a small (less than 5) number of monolayers, the differences between the predictions of these simpler models, and our approach, are important. Methods to improve the accuracy in the evaluation of various quantum size effects are shortly discussed. Using quantum mechanical-electromagnetic analogies, our results can be used in the study of light propagation in dielectric wave guides
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