Two-dimensional Schroedinger operators with fast decaying potential and multidimensional $L_2$-kernel

TL;DR

This paper demonstrates how to construct explicit two-dimensional Schrödinger operators with rapidly decaying potentials and multidimensional L2-kernels using Moutard transformations.

Contribution

It introduces a method to explicitly generate such operators, expanding the understanding of their spectral properties.

Findings

Explicit examples of operators with desired properties

Application of Moutard transformations in spectral theory

Potential for further analytical and numerical studies

Abstract

Using Moutard transformations we show how explicit examples of two-dimensional Schroedinger operators with fast decaying potential and multidimensional $L_2$-kernel may be constructed