Quantitative observability for one-dimensional Schrödinger equations with potentials

2023/09/02 by Pei Su, Chenmin Sun, Su, Pei +3 · 3 citations
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paper · pdf · doi:10.48550/arxiv.2309.00963

Abstract

In this note, we prove the quantitative observability with an explicit control cost for the 1D Schrödinger equation over ℝ with real-valued, bounded continuous potential on thick sets. Our proof relies on different techniques for low-frequency and high-frequency estimates. In particular, we extend the large time observability result for the 1D free Schrodinger equation in Theorem 1.1 of Huang-Wang-Wang [20] to any short time. As another byproduct, we extend the spectral inequality of Lebeau-Moyano [27] for real-analytic potentials to bounded continuous potentials in the one-dimensional case.

Citations

• The Landis conjecture on exponential decay

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