Band edges of periodic Schrödinger operators are generically isolated and nondegenerate
Zhongkai Tao, Mengxuan Yang
Abstract
For periodic Schrödinger operators HV=-Δ+V with bounded real-valued potentials on Rd with d2, 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 Schrödinger operators.
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