AUTHOR=Erman Fatih , Turgut O. Teoman 

TITLE=Completeness relation in renormalized quantum systems

JOURNAL=Frontiers in Physics

VOLUME=Volume 13 - 2025

YEAR=2025

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2025.1695365

DOI=10.3389/fphy.2025.1695365

ISSN=2296-424X

ABSTRACT=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 an 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 the sudden perturbation of the support of the delta potential.