The Schr\"odinger Equation with a Moving Point Interaction in Three Dimensions
Andrea Posilicano
TL;DR
This paper advances the mathematical understanding of quantum systems with moving point interactions in three dimensions by improving the existence theorem for the associated Schrödinger evolution.
Contribution
It introduces new techniques to strengthen the existence results for Schrödinger operators with moving point interactions in three dimensions.
Findings
Enhanced existence theorem for unitary evolution
New mathematical techniques for point interactions
Improved understanding of quantum dynamics with moving singularities
Abstract
In the case of a single point interaction we improve, by different techniques, the existence theorem for the unitary evolution generated by a Schr\"odinger operator with moving point interactions obtained by Dell'Antonio, Figari and Teta.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Advanced Mathematical Modeling in Engineering · Numerical methods in inverse problems