翻訳と辞書 Words near each other ・ Lambeth London Borough Council election, 1968 ・ Lambeth London Borough Council election, 1971 ・ Lambeth London Borough Council election, 1974 ・ Lambeth London Borough Council election, 1978 ・ Lambeth London Borough Council election, 1982 ・ Lambeth London Borough Council election, 1986 ・ Lambeth London Borough Council election, 1990 ・ Lambeth London Borough Council election, 1994 ・ Lambeth London Borough Council election, 1998 ・ Lambeth London Borough Council election, 2002 ・ Lambeth London Borough Council election, 2006 ・ Lambeth London Borough Council election, 2010 ・ Lambeth London Borough Council election, 2014 ・ Lambeth London Borough Council elections ・ Lambert-Sigisbert Adam ・ Lambert-W step-potential ・ Lambertella ・ Lambertellinia ・ Lamberti ・ Lambertia ・ Lambertia echinata ・ Lambertia ericifolia ・ Lambertia fairallii ・ Lambertia formosa ・ Lambertia ilicifolia ・ Lambertia inermis ・ Lambertia multiflora ・ Lambertia orbifolia ・ Lambertia rariflora ・ Lambertia uniflora Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Lambert-W step-potential ： ウィキペディア英語版 Lambert-W step-potential The Lambert-W step-potential〔("The Lambert W-barrier - an exactly solvable confluent hypergeometric potential" )〕 affords the fifth – next to those of the harmonic oscillator plus centrifugal, the Coulomb plus inverse square, the Morse, and the inverse square root〔("Exact solution of the Schrödinger equation for the potential V0/√x" )〕 potentials – exact solution to the stationary one-dimensional Schrödinger equation in terms of the confluent hypergeometric functions.〔("Discretization of Natanzon potentials" )〕 The potential is given as :$V(x)\; =\; \backslash frac$. where $W$ is the Lambert function also known as the product logarithm. This is an implicitly elementary function that resolves the equation $We^W=z$. The Lambert $W$-potential is an asymmetric step of height $V\_0$ whose steepness and asymmetry are controlled by parameter $\backslash sigma$. If the space origin and the energy origin are also included, it presents a four-parametric specification of a more general five-parametric potential which is also solvable in terms of the confluent hypergeometric functions. This generalized potential, however, is a conditionally integrable one (that is, it involves a fixed parameter). ==Solution== The general solution of the one-dimensional Schrödinger equation for a particle of mass $m$ and energy $E$: :$\backslash frac+\backslash frac(E-V(x))\backslash psi=0$, for the Lambert $W$-barrier for arbitrary $V\_0$ and $\backslash sigma$ is written as :$\backslash psi(x)=z^e^\backslash left(\backslash frac-i\backslash fracu(z)\backslash right),\; z=W(e^)$, where $u(z)$ is the general solution of the scaled confluent hypergeometric equation :$u\text{'}\text{'}(z)+\backslash left(\backslash frac-is\backslash right)u\text{'}(z)+\backslash fracu(z)=0$ and the involved parameters are given as :$a=\backslash frac+\backslash frac,\; \backslash delta=2\backslash sigma\backslash sqrt\},\; s=2\backslash sigma\backslash sqrt\}$. A peculiarity of the solution is that each of the two fundamental solutions composing the general solution involves a combination of two confluent hypergeometric functions. If the quantum transmission above the Lambert $W$-potential is discussed, it is convenient to choose the general solution of the scaled confluent hypergeometric equation as :$u=c\_1(isz)^\_1F\_1$ and $U$ are the Kummer and Tricomi confluent hypergeometric functions, respectively. The two confluent hypergeometric functions are here chosen such that each of them stands for a separate wave moving in a certain direction. For a wave incident from the left, the reflection coefficient written in terms of the standard notations for the wave numbers :$k\_1=\backslash sqrt\},k\_2=\backslash sqrt\}$ reads :$R=e^\backslash frac(k\_1-k\_2)^2\backslash right)\}\}(k\_1+k\_2)^2\backslash right)\}\}$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lambert-W step-potential」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.