有中心扰动的类氢光谱
Hydrogenoid spectra with central perturbations
摘要：
通过Kre \u In-Višik-Birman扩展方案，与基于von Neumann理论的经典分析不同，我们再现了具有库仑中心（核）支撑的奇异微扰的三维类氢哈密顿量的所有自伴实现的构造和分类，以及具有半直线上的库仑势的薛定谔算子的所有自伴实现的构造和分类.这两个问题在技术上是等价的，尽管有时在文献中被自己处理。在此基础上，我们得到了确定每个自伴扩张本征值的公式，作为对非相对论类氢能级的修正。我们讨论在这方面的Kre \u <$n-Višik-Birman计划是更自然的产生的典型边界条件的自伴中心的扰动。
英文摘要：
Through the Kre\uın-Višik-Birman extension scheme, unlike the classical analysis based on von Neumann's theory, we reproduce the construction and classification of all self-adjoint realisations of three-dimensional hydrogenoid-like Hamiltonians with singular perturbation supported at the Coulomb centre (the nucleus), as well as of Schrödinger operators with Coulomb potentials on the half-line. These two problems are technically equivalent, albeit sometimes treated by their own in the the literature. Based on such scheme, we then recover the formula to determine the eigenvalues of each self-adjoint extension, as corrections of the non-relativistic hydrogenoid energy levels. We discuss in which respect the Kre\uın-Višik-Birman scheme is somewhat more natural in yielding the typical boundary condition of self-adjointness at the centre of the perturbation.
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