1,406 research outputs found
Siewert solutions of transcendental equations, generalized Lambert functions and physical applications
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
Semiconductor Quantum Wells with BenDaniel-Duke Boundary Conditions and Janus Nanorods
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
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
- …