周期系统的有限区间反问题新理论
New theory of periodical systems by finite interval inverse problem
摘要：
我们表明，间隙形成的机制具有共振性质。发现了特殊的实基本解，它们在整个空位区间的所有能量处具有周期与势的周期一致的纽结分布。根据这些解，共振隙的出现得到了最直接的解释：势的不断重复撞击导致禁区内的波幅呈指数增加（减少）。在允许的区域内，来自相对侧的类似的交替撞击是波浪拍击的原因。反演技术产生了区域控制算法-移动光谱带的选定边界，改变区域禁止的程度。这一切都是以前的Bloch理论所不能达到的。
英文摘要：
We show that the mechanism of gap formation has a resonance nature. The special real fundamental solutions were discovered which `paradoxically' have knot distribution with a period coinciding with that of potential at all energies of the whole lacuna interval. In terms of these solutions resonance gap appearance gets the most direct explanation: ever repeating hits by the potential result in exponential increase (decrease) of the wave amplitudes in the forbidden zones. The analogous alternating hits from opposite sides are responsible for the wave beatings in allowed zones. The inversion technique gives rise to zone control algorithms - shifting chosen boundaries of spectral bands, changing degree of zone forbiddenness. All this cannot be achieved by the previous Bloch theory.
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