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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 Two-state quantum system ： ウィキペディア英語版 Two-state quantum system In quantum mechanics, a two-state system (also known as a two-level system) is a system which can exist in any quantum superposition of two independent (physically distinguishable) quantum states. The Hilbert space describing such a system is two-dimensional. Therefore, a complete basis spanning the space will consist of two independent states. Two-state systems are the simplest quantum systems that can exist, since the dynamics of a one-state system is trivial (i.e. there is no other state the system can exist in). The mathematical framework required for the analysis of two-state systems is that of linear differential equations and linear algebra of two-dimensional spaces. As a result, the dynamics of a two-state system can be solved analytically without any approximation. A very well known example of a two-state system is the spin of a spin-1/2 particle such as an electron, whose spin can have values +''ħ''/2 or −''ħ''/2, where ''ħ'' is the reduced Planck constant. Another example, frequently studied in atomic physics, is the transition of an atom to or from an excited state; here the two-state formalism is used to quantitatively explain stimulated and spontaneous emission of photons from excited atoms. ==Representation of the Two-state quantum system== The state of a two-state quantum system can be represented as vectors of a two-dimensional complex Hilbert space, this means every state vector $\backslash vert\backslash psi\backslash rangle$ is represented by two complex coordinates. :$|\backslash psi\backslash rangle\; =\; \backslash begin\; c\_1\; \backslash \backslash \; c\_2\backslash end\; =\; c\_1\backslash begin\; 1\; \backslash \backslash \; 0\backslash end\; +\; c\_2\backslash begin\; 0\; \backslash \backslash \; 1\backslash end\; ;$ where, $c\_1$ and $c\_2$ are the coordinates. If the vectors are normalized, $c\_1$ and $c\_2$ are related by $^2+^2\; =\; 1$ . the basis vectors will be represented as $|0\backslash rangle\; =\; \backslash begin\; 1\; \backslash \backslash \; 0\backslash end$ and $|1\backslash rangle\; =\; \backslash begin\; 0\; \backslash \backslash \; 1\backslash end$ All observable physical quantities associated with this systems are 2 $\backslash times$ 2 Hermitian matrices, this means the Hamiltonian of the system is also a similar matrix. 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「Two-state quantum system」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.