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In quantum physics, quantum state refers to the state of a quantum system. A quantum state can be either pure or mixed. A pure quantum state is represented by a vector, called a state vector, in a Hilbert space. For example, when dealing with the energy spectrum of the electron in a hydrogen atom, the relevant state vectors are identified by the principal quantum number, written . For a more complicated case, consider Bohm's formulation of the EPR experiment, where the state vector : involves superposition of joint spin states for two particles. Mathematically, a pure quantum state is represented by a state vector in a Hilbert space over complex numbers, which is a generalization of our more usual three-dimensional space.〔Griffiths, D.J.(2004), pp. 93–96.〕 If this Hilbert space is represented as a function space, then its elements are called wave functions. A mixed quantum state corresponds to a probabilistic mixture of pure states; however, different distributions of pure states can generate equivalent (i.e., physically indistinguishable) mixed states. Mixed states are described by so-called density matrices. A pure state can also be recast as a density matrix; in this way, pure states can be represented as a subset of the more general mixed states. For example, if the spin of an electron is measured in any direction, e.g. with a Stern–Gerlach experiment, there are two possible results: up or down. The Hilbert space for the electron's spin is therefore two-dimensional. A pure state here is represented by a two-dimensional complex vector , with a length of one; that is, with : where and are the absolute values of and . A mixed state, in this case, is a matrix that is Hermitian, positive-definite, and has trace 1. Before a particular measurement is performed on a quantum system, the theory usually gives only a probability distribution for the outcome, and the form that this distribution takes is completely determined by the quantum state and the observable describing the measurement. These probability distributions arise for both mixed states and pure states: it is impossible in quantum mechanics (unlike classical mechanics) to prepare a state in which all properties of the system are fixed and certain. This is exemplified by the uncertainty principle, and reflects a core difference between classical and quantum physics. Even in quantum theory, however, for every observable there are some states that have an exact and determined value for that observable.〔Griffiths, D.J.(2004), pp. 4–5.〕 ==Conceptual description== 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「quantum state」の詳細全文を読む スポンサード リンク
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