Uniqueness Results for Schroedinger Operators on the Line with Purely Discrete Spectra

Abstract

We provide an abstract framework for singular one-dimensional Schroedinger operators with purely discrete spectra to show when the spectrum plus norming constants determine such an operator completely. As an example we apply our findings to prove a new uniqueness results for perturbed quantum mechanical harmonic oscillators. In addition, we also show how to establish a Hochstadt-Liebermann type result for these operators. Our approach is based on the singular Weyl-Titchmarsh theory which is extended to cover the present situation.

19 pages

Cited by in corpus (10)

• Uniqueness for Inverse Sturm-Liouville Problems with a Finite Number of Transmission Conditions
• On the isospectral problem of the dispersionless Camassa-Holm equation
• Inverse square singularities and eigenparameter dependent boundary conditions are two sides of the same coin
• Singular Weyl-Titchmarsh-Kodaira theory for one-dimensional Dirac operators
• Spectral Asymptotics for Perturbed Spherical Schrödinger Operators and Applications to Quantum Scattering
• On Spectral Deformations and Singular Weyl Functions for One-Dimensional Dirac Operators
• Direct and inverse spectral theorems for a class of canonical systems with two singular endpoints
• Singular Schroedinger operators as self-adjoint extensions of n-entire operators
• A class of $n$-entire Schrödinger operators
• A survey of non-uniqueness results for the anisotropic Calder{ó}n problem with disjoint data