论文标题
Klein-Gordon操作员的连续光谱中没有特征值
Absence of eigenvalues in the continuous spectrum for Klein-Gordon operators
论文作者
论文摘要
我们构建了von-neumann Wigner的一维类似于相对论的klein-gordon操作员，在该操作员中，定义的是采用渐近数学规则，以获得嵌入在连续光谱中的特征值的存在条件。利用我们的构造潜力，我们提供了一个具有正面特征值的klein-gordon操作员的明确和分析示例，该特征值嵌入了所谓的相对论“连续性区域”。即使在这个不是标准的示例中，我们也介绍了无法发生这些特征值的“连续体”的区域。此外，在连续光谱中缺乏克莱恩 - 戈登操作员的特征值已被证明是广泛的一般潜在类别，包括最小耦合的电库仑电位。考虑到Schrodinger操作员文献中可用的已知技术，我们演示了以Schrodinger形式编写的Klein-Gordon操作员的表达，从而确定了缺乏特征值的数学谱系区域。
We construct the one-dimensional analogous of von-Neumann Wigner potential to the relativistic Klein-Gordon operator, in which is defined taking asymptotic mathematical rules in order to obtain existence conditions of eigenvalues embedded in the continuous spectrum. Using our constructed potential, we provide an explicit and analytical example of the Klein-Gordon operator with positive eigenvalues embedded in the so called relativistic "continuum region". Even so in this not standard example, we present the region of the "continuum" where those eigenvalues cannot occur. Besides, the absence of eigenvalues in the continuous spectrum for Klein-Gordon operators is proven to a broad general potential classes, including the minimally coupled electric Coulomb potential. Considering known techniques available in literature for Schrodinger operators, we demonstrate an expression for Klein-Gordon operator written in Schrodinger's form, whereby is determined the mathematical spectrum region of absence of eigenvalues.
