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arXiv · 1110.2453

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

Jonathan Eckhardt·Gerald Teschl
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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.

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Jonathan Eckhardt, Gerald Teschl. 2011-10-11. Uniqueness Results for Schroedinger Operators on the Line with Purely Discrete Spectra. https://doi.org/10.1090/s0002-9947-2012-05821-1

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