Related papers: Completeness Relation in Renormalized Quantum Systems

Completeness Relation in Renormalized Quantum Systems

URL: http://arxiv.org/abs/2409.05372v1
Date: Mon, 9 Sep 2024 07:09:16 GMT
Title: Completeness Relation in Renormalized Quantum Systems
Authors: Fatih Erman, O. Teoman Turgut,
Abstract summary: We show that the completeness relation for the eigenvectors, which is an essential assumption of quantum mechanics, remains true if the initial Hamiltonian, having a discrete spectrum, is modified by a delta potential. 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.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
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 initial 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.

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