Band edges of periodic Schr\"odinger operators are generically isolated and nondegenerate

Zhongkai Tao; Mengxuan Yang

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arXiv · 2608.30189

Band edges of periodic Schr\"odinger operators are generically isolated and nondegenerate

Zhongkai Tao·Mengxuan Yang

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Abstract

For periodic Schr\"odinger operators $H_V=-\Delta+V$ with bounded real-valued potentials on $\mathbb R^d$ with $d\ge2$, we show that for generic potentials, each endpoint of every spectral gap is attained by a single Bloch band at only finitely many quasimomenta, and has a nondegenerate Hessian at every attaining point. This proves the Spectral Edge Conjecture for periodic Schr\"odinger operators.

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BibTeX RIS

Zhongkai Tao, Mengxuan Yang. 2026-08-31. Band edges of periodic Schr\"odinger operators are generically isolated and nondegenerate. https://arxiv.org/abs/2608.30189

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