翻訳と辞書 Words near each other ・ Fractional horsepower motor ・ Fractional ideal ・ Fractional Importance ・ Fractional kill ・ Fractional lambda switching ・ Fractional Orbital Bombardment System ・ Fractional ownership ・ Fractional ownership of aircraft ・ Fractional part ・ Fractional Poisson process ・ Fractional programming ・ Fractional quantum Hall effect ・ Fractional quantum mechanics ・ Fractional renting ・ Fractional rig ・ Fractional Schrödinger equation ・ Fractional sodium excretion ・ Fractional supersymmetry ・ Fractional vortices ・ Fractional wavelet transform ・ Fractional-order control ・ Fractional-order integrator ・ Fractional-order system ・ Fractional-reserve banking ・ Fractionalism ・ Fractionalization ・ Fractionated spacecraft ・ Fractionating column ・ Fractionation ・ Fractionation Research Inc. 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 Fractional Schrödinger equation ： ウィキペディア英語版 Fractional Schrödinger equation (詳細はfractional quantum mechanics. It was discovered by Nick Laskin (1999) as a result of extending the Feynman path integral, from the Brownian-like to Lévy-like quantum mechanical paths. The term ''fractional Schrödinger equation'' was coined by Nick Laskin.〔N. Laskin, (2000), ( Fractional Quantum Mechanics and Lévy Path Integrals. ''Physics Letters'' 268A, 298-304 ).〕 ==Fundamentals== The fractional Schrödinger equation in the form originally obtained by Nick Laskin is:〔N. Laskin, (2002), (Fractional Schrödinger equation, ''Physical Review'' E66, 056108 7 pages ). '' (also available online: http://arxiv.org/abs/quant-ph/0206098)〕 *r is the 3-dimensional position vector, *''ħ'' is the reduced Planck constant, *''ψ''(r, ''t'') is the wavefunction, which is the quantum mechanical probability amplitude for the particle to have a given position r at any given time ''t'', *''V''(r, ''t'') is a potential energy, *Δ = ∂2/∂r2 is the Laplace operator. Further, *''Dα'' is a scale constant with physical dimension () = ()1 − ''α''·()''α''()−''α'', at ''α'' = 2, ''D''2 =1/2''m'', where ''m'' is a particle mass, *the operator (−''ħ''2Δ)''α''/2 is the 3-dimensional fractional quantum Riesz derivative defined by (see, Ref.()); ::$$ (-\hbar ^2\Delta )^\psi (\mathbf,t)=\frac 1\int d^3pe^|\mathbf|^\alpha \varphi ( \mathbf,t), Here, the wave functions in the position and momentum spaces; $\backslash psi(\backslash mathbf,t)$ and $\backslash varphi\; (\backslash mathbf,t)$ are related each other by the 3-dimensional Fourier transforms: :$$ \psi (\mathbf,t)=\frac 1\int d^3pe^/\hbar}\varphi (\mathbf,t),\qquad \varphi (\mathbf,t)=\int d^3re^/\hbar }\psi (\mathbf,t). The index ''α'' in the fractional Schrödinger equation is the Lévy index, 1 < ''α'' ≤ 2. Thus, the fractional Schrödinger equation includes a space derivative of fractional order ''α'' instead of the second order (''α'' = 2) space derivative in the standard Schrödinger equation. Thus, the fractional Schrödinger equation is a fractional differential equation in accordance with modern terminology.〔S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications ~Gordon and Breach, Amsterdam, 1993〕 This is the main point of the term ''fractional Schrödinger equation'' or a more general term fractional quantum mechanics.〔N. Laskin, (2000), (Fractional Quantum Mechanics, ''Physical Review'' E62, 3135-3145 ). '' (also available online: http://arxiv.org/abs/0811.1769)〕 At ''α'' = 2 fractional Schrödinger equation becomes the well-known Schrödinger equation. The fractional Schrödinger equation has the following operator form where the fractional Hamilton operator $\backslash widehat\_\backslash alpha$ is given by : $$ \widehat_\alpha =D_\alpha (-\hbar ^2\Delta )^+V(\mathbf,t). The Hamilton operator, $\backslash widehat\_\backslash alpha$ corresponds to the classical mechanics Hamiltonian function introduced by Nick Laskin : $$ H_\alpha (\mathbf,\mathbf)=D_\alpha |\mathbf|^\alpha +V(\mathbf,t), where p and r are the momentum and the position vectors respectively. 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「Fractional Schrödinger equation」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.