Schr\"{o}dinger operators with distributional potentials and boundary conditions dependent on the eigenvalue parameter

TL;DR

This paper investigates spectral problems for one-dimensional Schrödinger equations with distributional potentials and boundary conditions that depend on the eigenvalue, advancing understanding of such complex quantum systems.

Contribution

It introduces new methods for analyzing spectral problems involving distributional potentials and eigenvalue-dependent boundary conditions in one-dimensional Schrödinger operators.

Findings

Development of techniques for direct spectral analysis

Solutions to inverse spectral problems with distributional potentials

Characterization of boundary conditions dependent on eigenvalues

Abstract

We study various direct and inverse spectral problems for the one-dimensional Schr\"{o}dinger equation with distributional potential and boundary conditions containing the eigenvalue parameter.