Uniqueness Results for Schroedinger Operators on the Line with Purely Discrete Spectra
arXiv:1110.2453 · doi:10.1090/S0002-9947-2012-05821-1
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