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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 Stationary state ： ウィキペディア英語版 Stationary state In quantum mechanics, a stationary state is an eigenvector of the Hamiltonian, implying the probability density associated with the wavefunction is independent of time.〔Quantum Mechanics Demystified, D. McMahon, Mc Graw Hill (USA), 2006, ISBN 0-07-145546-9〕 This corresponds to a quantum state with a single definite energy (instead of a quantum superposition of different energies). It is also called energy eigenvector, energy eigenstate, energy eigenfunction, or energy eigenket. It is very similar to the concept of atomic orbital and molecular orbital in chemistry, with some slight differences explained below. ==Introduction== A stationary state is called ''stationary'' because the system remains in the same state as time elapses, in every observable way. For a single-particle Hamiltonian, this means that the particle has a constant probability distribution for its position, its velocity, its spin, etc.〔Cohen-Tannoudji, Claude, Bernard Diu, and Franck Laloë. ''Quantum Mechanics: Volume One''. Hermann, 1977. p. 32.〕 (This is true assuming the particle's environment is also static, i.e. the Hamiltonian is unchanging in time.) The wavefunction itself is not stationary: It continually changes its overall complex phase factor, so as to form a standing wave. The oscillation frequency of the standing wave, times Planck's constant, is the energy of the state according to the Planck–Einstein relation. Stationary states are quantum states that are solutions to the time-independent Schrödinger equation: :$\backslash hat\; H\; |\backslash Psi\backslash rangle=E\_\; |\backslash Psi\backslash rangle$, where *$|\backslash Psi\backslash rangle$ is a quantum state, which is a stationary state if it satisfies this equation; *$\backslash hat\; H$ is the Hamiltonian operator; *$E\_$ is a real number, and corresponds to the energy eigenvalue of the state $|\backslash Psi\backslash rangle$. This is an eigenvalue equation: $\backslash hat\; H$ is a linear operator on a vector space, $|\backslash Psi\backslash rangle$ is an eigenvector of $\backslash hat\; H$, and $E\_$ is its eigenvalue. If a stationary state $|\backslash Psi\backslash rangle$ is plugged into the time-dependent Schrödinger Equation, the result is:〔Quanta: A handbook of concepts, P.W. Atkins, Oxford University Press, 1974, ISBN 0-19-855493-1〕 :$i\backslash hbar\backslash frac\; |\backslash Psi\backslash rangle\; =\; E\_|\backslash Psi\backslash rangle$ Assuming that $\backslash hat\; H$ is time-independent (unchanging in time), this equation holds for any time ''t''. Therefore this is a differential equation describing how $|\backslash Psi\backslash rangle$ varies in time. Its solution is: :$|\backslash Psi(t)\backslash rangle\; =\; e^|\backslash Psi(0)\backslash rangle$ Therefore a stationary state is a standing wave that oscillates with an overall complex phase factor, and its oscillation angular frequency is equal to its energy divided by $\backslash hbar$. 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「Stationary state」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.