具有拟周期扰动的谐振子本征值的渐近性
Asymptotics for the Eigenvalues of the Harmonic Oscillator with a Quasi-Periodic Perturbation
摘要：
我们考虑H+V形式的算子，其中H是一维谐振子，V是零阶伪微分算子，在适当的意义下是准周期的（例如，可以将V乘以周期函数）。本文证明了H+V的特征值具有渐近性：λ n（H+V）=λ n（H）+W（\sqrt n）n^{-1/4}+O（n^{-1/2} \ln（n））as \to + \infty，其中W是一个可用V明确定义的准周期函数.
英文摘要：
We consider operators of the form H+V where H is the one-dimensional harmonic oscillator and V is a zero-order pseudo-differential operator which is quasi-periodic in an appropriate sense (one can take V to be multiplication by a periodic function for example). It is shown that the eigenvalues of H+V have asymptotics of the form λ_n(H+V)=λ_n(H)+W(\sqrt n)n^{-1/4}+O(n^{-1/2}\ln(n)) as n\to+\infty, where W is a quasi-periodic function which can be defined explicitly in terms of V.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
