Tutorial: The quantum finite square well and the Lambert W function
نویسندگان
چکیده
منابع مشابه
The Lambert W Function
has a countably infinite number of solutions, which are denoted by Wk(z) for integers k. Each choice of k specifies a branch of the Lambert W function. By convention, only the branches k = 0 (called the principal branch) and k = −1 are real-valued for any z; the range of every other branch excludes the real axis, although the range of W1(z) includes (−∞,−1/e] in its closure. Only W0(z) contains...
متن کاملExplicit infiltration equations and the Lambert W-function
The Green and Ampl infiltration formula. as well as the T,llsmll and Parlangc formula. arc two-parameter equations that arc both expressible in h::rms of Lambert IV-functions. These representations are used to derive explicit. simple and accurate approximations for each CllSl.'. The IWO infiltmlion fonnulas are limiting caSt-os that can be deduced from an existing three.par.lmeter in· filtmtion...
متن کاملGeneral Relativity and Quantum Mechanics: Towards a Generalization of the Lambert W Function
Herein, we present a canonical form for a natural and necessary generalization of the Lambert W function, natural in that it requires minimal mathematical definitions for this generalization, and necessary in that it provides a means of expressing solutions to a number of physical problems of fundamental nature. In particular, this generalization expresses the exact solutions for general-relati...
متن کاملOn the Lambert W function: EOQ applications and pedagogical considerations
The Lambert W function dates back to Euler’s time and despite offering solutions to many operations management problems it is still relatively unknown. This may be due to the fact that it is only incorporated into specialist mathematical software and is not generally available in common spreadsheet applications. This obscurity is rather unfortunate as it is relatively easy to use when the signi...
متن کاملLambert W Function in Hydraulic Problems ∗
Darcy’s flow friction factor is expressed in implicit form in some of the relations such as Colebrook’s and have to be solved by iteration procedure because the unknown friction factor appears on both sides of the equation. Lambert W function is implicitly elementary but is not, itself, an elementary function. Implicit form of the Lambert W function allows us to transform other implicit functio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Canadian Journal of Physics
سال: 2017
ISSN: 0008-4204,1208-6045
DOI: 10.1139/cjp-2016-0602