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arXiv · 2209.12220

Asymptotic expansion of the spectrum for periodic Schr\"{o}dinger operators

Scott Armstrong·Raghavendra Venkatraman
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Abstract

We prove an asymptotic expansion for the eigenvalues and eigenfunctions of Schr\"{o}dinger-type operator with a confining potential and with principle part a periodic elliptic operator in divergence form. We compare the spectrum to the homogenized operator and characterize the corrections up to arbitrarily high order.

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Scott Armstrong, Raghavendra Venkatraman. 2022-09-25. Asymptotic expansion of the spectrum for periodic Schr\"{o}dinger operators. https://arxiv.org/abs/2209.12220

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