Singular Perturbations, Regularization and Extension Theory
H. Neidhardt, V. A. Zagrebnov
TL;DR
This paper investigates the mathematical relationship between regularization techniques and self-adjoint extensions for Schrödinger operators with singular, non-semibounded potentials, providing abstract theoretical insights.
Contribution
It establishes a connection between regularizations and self-adjoint extensions for singular potentials that are not semibounded from below.
Findings
Characterizes the relation between regularizations and self-adjoint extensions.
Provides an abstract framework for removing regularization in singular potentials.
Enhances understanding of Schrödinger operators with non-semibounded singularities.
Abstract
We present an abstract result on removing regularization for singular potentials which are not semibounded from below. The relation between ``right'' regularizations and ``right'' self-adjoint extensions of the perturbed Schr\"odinger operators is examined.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Numerical methods in inverse problems · Quantum Mechanics and Non-Hermitian Physics