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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 Method of quantum characteristics ： ウィキペディア英語版 Method of quantum characteristics Quantum characteristics are phase-space trajectories that arise in the phase space formulation of quantum mechanics through the Wigner transform of Heisenberg operators of canonical coordinates and momenta. These trajectories obey the Hamilton equations in quantum form and play the role of characteristics in terms of which time-dependent Weyl's symbols of quantum operators can be expressed. In the classical limit, quantum characteristics reduce to classical trajectories. The knowledge of quantum characteristics is equivalent to the knowledge of quantum dynamics. == Weyl-Wigner association rule == In Hamiltonian dynamics, classical systems with $n$ degrees of freedom are described by $2n$ canonical coordinates and momenta :$^\backslash xi^\; =\; (x^1,\; .\; .\; .\; ,\; x^n,\; p\_1,\; .\; .\; .\; ,\; p\_n)\; \backslash in\; \backslash mathbb^,$ that form a coordinate system in the phase space. These variables satisfy the Poisson bracket relations :$^\backslash \backslash \}=-I^.$ The skew-symmetric matrix $^I^$, :$\backslash left\backslash |\; I\backslash right\backslash |\; =\backslash left\backslash |$ \begin 0 & -E_ \\ E_ & 0 \end \right\|, where $^E\_n$ is the $n\; \backslash times\; n$ identity matrix, defines nondegenerate 2-form in the phase space. The phase space acquires thereby the structure of a symplectic manifold. The phase space is not metric space, so distance between two points is not defined. The Poisson bracket of two functions can be interpreted as the oriented area of a parallelogram whose adjacent sides are gradients of these functions. Rotations in Euclidean space leave the distance between two points invariant. Canonical transformations in symplectic manifold leave the areas invariant. In quantum mechanics, the canonical variables $^\backslash xi$ are associated to operators of canonical coordinates and momenta :$\backslash hat^\; =\; (\backslash hat^1,\; .\; .\; .\; ,\; \backslash hat^n,\; \backslash hat\_1,\; .\; .\; .\; ,\; \backslash hat\_n)\; \backslash in\; \backslash operatorname(L^2(\backslash mathbb^n)).$ These operators act in Hilbert space and obey commutation relations :$()=-i\backslash hbar\; I^.$ Weyl’s association rule〔H. Weyl, Z. Phys. 46, 1 (1927).〕 extends the correspondence $\backslash xi^i\; \backslash rightarrow\; \backslash hat^i$ to arbitrary phase-space functions and operators. 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「Method of quantum characteristics」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.