计算周期算子谱的通用算法
Universal algorithms for computing spectra of periodic operators
摘要：
薛定谔算子与周期（可能复值）的潜力和离散周期运营商（可能与复值条目）被认为是，并在这两种情况下的计算谱问题进行调查：即，在什么条件下可以设计一个“一刀切”的算法计算其频谱？结果表明，对于周期带状矩阵，这是可以做到的，以及薛定谔运营商的周期潜力是足够光滑的。在这两种情况下，提供了可实现的算法，以及示例。对于某些薛定谔算子，其势可能在一个点发散（但在其他方面表现良好），它表明，不存在这样的算法，虽然它表明，计算是可能的，如果一个允许两个连续的限制。
英文摘要：
Schrödinger operators with periodic (possibly complex-valued) potentials and discrete periodic operators (possibly with complex-valued entries) are considered, and in both cases the computational spectral problem is investigated: namely, under what conditions can a "one-size-fits-all" algorithm for computing their spectra be devised? It is shown that for periodic banded matrices this can be done, as well as for Schrödinger operators with periodic potentials that are sufficiently smooth. In both cases implementable algorithms are provided, along with examples. For certain Schrödinger operators whose potentials may diverge at a single point (but are otherwise well-behaved) it is shown that there does not exist such an algorithm, though it is shown that the computation is possible if one allows for two successive limits.
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