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Born–von Karman boundary conditions are periodic boundary conditions which impose the restriction that a wave function must be periodic on a certain Bravais lattice. (Named after Max Born and Theodore von Kármán). This condition is often applied in solid state physics to model an ideal crystal. The condition can be stated as : where ''i'' runs over the dimensions of the Bravais lattice, the a''i'' are the primitive vectors of the lattice, and the ''Ni'' are integers (assuming the lattice has ''N'' cells where ''N=N1N2N3''). This definition can be used to show that : for any lattice translation vector T such that: : Note, however, the Born–von Karman boundary conditions are useful when ''Ni'' are large (infinite). The Born–von Karman boundary condition is important in solid state physics for analyzing many features of crystals, such as diffraction and the band gap. Modeling the potential of a crystal as a periodic function with the Born–von Karman boundary condition and plugging in Schrödinger's equation results in a proof of Bloch's theorem, which is particularly important in understanding the band structure of crystals. ==References== * * 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「Born–von Karman boundary condition」の詳細全文を読む スポンサード リンク
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