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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Klein–Gordon equation ： ウィキペディア英語版 Klein–Gordon equation The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic version of the Schrödinger equation. Its solutions include a quantum scalar or pseudoscalar field, a field whose quanta are spinless particles. It cannot be straightforwardly interpreted as a Schrödinger equation for a quantum state, because it is second order in time and because it does not admit a positive definite conserved probability density. Still, with the appropriate interpretation, it does describe the quantum amplitude for finding a point particle in various places, the relativistic wavefunction, but the particle propagates both forwards and backwards in time. Any solution to the Dirac equation is automatically a solution to the Klein–Gordon equation, but the converse is not true. ==Statement== The Klein–Gordon equation is :$\backslash frac\; \backslash frac\; \backslash psi\; -\; \backslash nabla^2\; \backslash psi\; +\; \backslash frac\; \backslash psi\; =\; 0.$ This is often abbreviated as :$(\backslash Box\; +\; \backslash mu^2)\; \backslash psi\; =\; 0,$ where and is the d'Alembert operator, defined by :$\backslash Box\; =\; -\backslash eta^\; \backslash partial\_\backslash mu\; \backslash partial\_\backslash nu\; =\; \backslash frac\backslash frac\; -\; \backslash nabla^2.$ (We are using the (−, +, +, +) metric signature.) The Klein-Gordon equation is most often written in natural units: :$-\; \backslash partial\_t^2\; \backslash psi\; +\; \backslash nabla^2\; \backslash psi\; =\; m^2\; \backslash psi$ The form is determined by requiring that plane wave solutions of the equation: :$\backslash psi\; =\; e^\; =\; e^$ obey the energy momentum relation of special relativity: :$-p\_\backslash mu\; p^\backslash mu\; =\; E^2\; -\; P^2\; =\; \backslash omega^2\; -\; k^2\; =\; -\; k\_\backslash mu\; k^\backslash mu\; =\; m^2$ Unlike the Schrödinger equation, the Klein–Gordon equation admits two values of for each , one positive and one negative. Only by separating out the positive and negative frequency parts does one obtain an equation describing a relativistic wavefunction. For the time-independent case, the Klein–Gordon equation becomes :$\backslash left(\backslash nabla^2\; -\; \backslash frac\; \backslash right)\; \backslash psi(\backslash mathbf)\; =\; 0$ which is the homogeneous screened Poisson equation. 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「Klein–Gordon 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.