Gap of the First Two Eigenvalues of the Schrödinger Operator with Nonconvex Potential

2009/02/13 by Shing-Tung Yau, Shing–Tung Yau, Yau, Shing-Tung
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.0902.2253

arxiv created 2009/02/13 · openalex publication_date 2009/02/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a lower estimate of the gap of the first two eigenvalues of the Schrodinger operator with a nonconvex potential in terms of a distance associated with the potential. The results here can be applied to the double well potential.

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