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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 Operator (physics) ： ウィキペディア英語版 Operator (physics) In physics, an operator is a function over the space of physical states. As a result of its application on a physical state, another physical state is obtained, very often along with some extra relevant information. The simplest example of the utility of operators is the study of symmetry. Because of this, they are a very useful tool in classical mechanics. In quantum mechanics, on the other hand, they are an intrinsic part of the formulation of the theory. ==Operators in classical mechanics== In classical mechanics, the movement of a particle (or system of particles) is completely determined by the Lagrangian $L(q,\; \backslash dot,\; t)$ or equivalently the Hamiltonian $H(q,\; p,\; t)$, a function of the generalized coordinates ''q'', generalized velocities $\backslash dot\; =\; \backslash mathrm\; q\; /\; \backslash mathrm\; t$ and its conjugate momenta: :$p\; =\; \backslash frac\{\backslash partial\; \backslash dot\{q\}\}$ If either ''L'' or ''H'' are independent of a generalized coordinate ''q'', meaning the ''L'' and ''H'' do not change when ''q'' is changed, which in turn means the dynamics of the particle are still the same even when ''q'' changes, the corresponding momenta conjugate to those coordinates will be conserved (this is part of Noether's theorem, and the invariance of motion with respect to the coordinate ''q'' is a symmetry). Operators in classical mechanics are related to these symmetries. More technically, when ''H'' is invariant under the action of a certain group of transformations ''G'': :$S\backslash in\; G,\; H(S(q,p))=H(q,p)$. the elements of ''G'' are physical operators, which map physical states among themselves. 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「Operator (physics)」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.