Perturbation series for the Schrödinger operator with a periodic potential near planes of diffraction
Perturbation series for the Schrödinger operator with a periodic potential near planes of diffraction
复制标题
衍射平面附近具有周期性势的薛定谔算子的扰动级数
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
Yulia Karpeshina
中科院分区：
文献类型：
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作者：
Yulia Karpeshina
在L2（R）中），其中V是乘以周期势的算子，三角多项式。在文献[1]和[2]中，Bloch特征值和谱投影的扰动级数是在一个丰富的拟动量集上构造的。在这个集合上，扰动和未扰动的特征值和谱投影是接近的。我们的目的是研究晶体中存在真实的折射的情况，即，扰动是显著的。也就是说，我们构造了劳厄衍射面附近的准动量微扰公式。我们描述布洛赫本征值和他们的光谱投影，如果，这是接近一些模型运营商，大致考虑到晶体内的折射。为了简化符号，我们考虑周期单元正交的情况。所有参数都经过了明显的修改，
in L2(R)) where V is the operator of multiplication by a periodic potential, a trigonometric polynomial. In [1] and [2], perturbation series for Bloch eigenvalues and spectral projections were constructed on a rich set of quasimomenta. On this set, the perturbed and unperturbed eigenvalues and spectral projectors turn out to be close. Our aim here is to study the case when there exists a real refraction in the crystal, i.e., the perturbation is significant. Namely, we construct perturbation formulae for quasimomenta in a vicinity of the Laue diffraction planes. We describe Bloch eigenvalues and their spectral projections of if, which are close to those of some model operator, roughly taking into account the refraction inside the crystal. To simplify notation, we consider the case where the cell of periods is orthogonal. All arguments go through, with obvious modifications, for a