重整化量子系统中的完备性关系
Completeness Relation in Renormalized Quantum Systems
AI总结：
本文证明经重整化δ势修正的离散谱哈密顿量仍满足量子力学本征矢完备性关系，将结论推广至多类δ势场景，并给出其在突然微扰问题中的应用。
摘要：
本研究表明，本征矢量的完备性关系作为量子力学的核心假设，当具有离散谱的哈密顿量经支撑于二维、三维紧流形或欧氏空间单点处的δ势（通过重整化方案严格定义）修正后仍然成立。该表述可轻松推广到N中心情形，以及δ相互作用支撑于平面或空间中曲线的情形。最后我们给出了该结论在δ势支撑集的突然微扰问题中的一个有趣应用。
英文摘要：
In this work, we show that the completeness relation for the eigenvectors, which is an essential assumption of quantum mechanics, remains true if the Hamiltonian, having a discrete spectrum, is modified by a delta potential (to be made precise by a renormalization scheme) supported at a point in two and three-dimensional compact manifolds or Euclidean spaces. The formulation can be easily extended to $N$ center case, and the case where delta interaction is supported on curves in the plane or space. We finally give an interesting application for sudden perturbation of the support of the delta potential.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
