类平方反比势薛定谔方程的实用SAE方法
Pragmatic SAE procedure in the Schrodinger equation for the inverse-square-like potentials
摘要：
本文评述了在原点表现为吸引平方反比势的薛定谔方程的自伴延拓。还提供了原始结果。证明了在一定的参数区间内，附加的非正则解必须保留，这就需要对径向Hamilton算子进行自伴延拓（SAE）.本文采用了实用方法，并考虑了它对大类传递势的一些结果.我们的考虑是基于我们早先建立的径向波函数的边界条件，并导出了相应的结果。还介绍了各种相关应用。它们是：在保留附加非正则解的情况下，求解薛定谔方程中的平方反比势。考虑价电子模型和带库仑势的Klein-Gordon方程，讨论了类分数氢能级。
英文摘要：
The Self-Adjoint Extension in the Schrodinger equation for potentials behaved as an attractive inverse square at the origin is critically reviewed. Original results are also presented. It is shown that the additional non-regular solutions must be retained for definite interval of parameters, which requires a necessity of performing a Self-Adjoint Extension (SAE) procedure of radial Hamiltonian.The Pragmatic approach is used and some of its consequences are considered for wide class of transitive potentials. Our consideration is based on the established earlier by us a boundary condition for the radial wave function and the corresponding consequences are derived. Various relevant applications are presented as well. They are: inverse square potential in the Schrodinger equation is solved when the additional non-regular solution is retained. Valence electron model and the Klein-Gordon equation with the Coulomb potential is considered and the hydrino -like levels are discussed.
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