One-dimensional Stark operators in the half-line

TL;DR

This paper derives asymptotic formulas for the spectral data of one-dimensional Stark operators with a perturbation, providing insights into their spectral properties under different boundary conditions.

Contribution

It introduces new asymptotic formulas for the spectral data of perturbed Stark operators on the half-line with Dirichlet or Neumann boundary conditions.

Findings

Asymptotic formulas for spectral data obtained

Results apply to operators with integrable perturbations

Spectral properties characterized for different boundary conditions

Abstract

We obtain asymptotic formulas for the spectral data of perturbed Stark operators associated with the differential expression \[ -\frac{d^2}{dx^2} + x + q(x), \quad x\in [0,\infty), \quad q\in L^1(0,\infty), \] and having either Dirichlet or Neumann boundary condition at the origin.