An improved bound for the ground state of a Schrödinger operator on a loop

2025/04/28 by Linde, Helmut
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2504.20229

Abstract

Consider a closed curve of length 2π with curvature κ(s) and the Schrödinger operator H with κ² as the potential term. Let λ_Γ be the lowest eigenvalue of H. The Ovals Conjecture proposed by Benguria and Loss states that λ_Γ≥ 1. While the conjecture remains open, the present work establishes a new lower bound of 0.81 on λ_Γ, improving on the previously best known estimate of 0.6085.

Citations

• Existence and Regularity for a Curvature Dependent Variational Problem
• A lower bound for the ground state energy of a Schroedinger operator on a loop
• On an isoperimetric inequality for a Schrodinger operator depending on the curvature of a loop

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