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The adiabatic theorem is a concept in quantum mechanics. Its original form, due to Max Born and Vladimir Fock (1928), was stated as follows: :''A physical system remains in its instantaneous eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest of the Hamiltonian's spectrum.'' In simpler terms, a quantum mechanical system subjected to gradually changing external conditions adapts its functional form, but when subjected to rapidly varying conditions there is insufficient time for the functional form to adapt, so the spatial probability density remains unchanged. == Diabatic vs. adiabatic processes == Diabatic process: Rapidly changing conditions prevent the system from adapting its configuration during the process, hence the spatial probability density remains unchanged. Typically there is no eigenstate of the final Hamiltonian with the same functional form as the initial state. The system ends in a linear combination of states that sum to reproduce the initial probability density. Adiabatic process: Gradually changing conditions allow the system to adapt its configuration, hence the probability density is modified by the process. If the system starts in an eigenstate of the initial Hamiltonian, it will end in the ''corresponding'' eigenstate of the final Hamiltonian. At some initial time a quantum-mechanical system has an energy given by the Hamiltonian ; the system is in an eigenstate of labelled . Changing conditions modify the Hamiltonian in a continuous manner, resulting in a final Hamiltonian at some later time . The system will evolve according to the Schrödinger equation, to reach a final state . The adiabatic theorem states that the modification to the system depends critically on the time during which the modification takes place. For a truly adiabatic process we require ; in this case the final state will be an eigenstate of the final Hamiltonian , with a modified configuration: :. The degree to which a given change approximates an adiabatic process depends on both the energy separation between and adjacent states, and the ratio of the interval to the characteristic time-scale of the evolution of for a time-independent Hamiltonian, , where is the energy of . Conversely, in the limit we have infinitely rapid, or diabatic passage; the configuration of the state remains unchanged: :. The so-called "gap condition" included in Born and Fock's original definition given above refers to a requirement that the spectrum of ''corresponds'' to ). In 1999 J. E. Avron and A. Elgart reformulated the adiabatic theorem, eliminating the gap condition. Note that the term "adiabatic" is traditionally used in thermodynamics to describe processes without the exchange of heat between system and environment (see adiabatic process). The quantum mechanical definition is closer to the thermodynamical concept of a quasistatic process, and has no direct relation with heat exchange. 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「Adiabatic theorem」の詳細全文を読む スポンサード リンク
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