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- W2008101604 abstract "The notion of effectively localized states for a finite one-dimensional array of identical square quantum-wells is introduced. A technique is described to determine the criterion for the existence of such localized states. The resulting criterion for arbitrary, but finite N, is given by f√V-E ⩾ 3.6 √Ea, where f represents barrier-to-well-width ratio, b/a (b is barrier width and a is well width), V denotes potential-well depth, E denotes particle eigenenergy, and Ea is written for the ground-state energy of a particle in an infinitely deep well of width a. At constant well width, f is a measure of the separation between wells and in this respect the preceding criterion resembles that relevant to the Mott transition in which the metal-insulator transition occurs at sufficiently large atomic separation. However, the transition from extended to effectively localized states in the present work is non-percolative and for this, as well as other reasons, is not representative of the Mott transition. A discussion is included of the relevance of the present analysis to the Hückel method in the LCAO approximation. It is further shown that Bloch's theorem does not apply to the present configuration." @default.
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- W2008101604 date "1993-03-01" @default.
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- W2008101604 title "Effectively localized states for a 1-d periodic array of arbitrary finite length" @default.
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- W2008101604 doi "https://doi.org/10.1016/0375-9601(93)90554-d" @default.
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