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تسجيل مستخدم جديدAsymptotics for the Eigenvalues of the Harmonic Oscillator with a Quasi-Periodic Perturbation
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Daniel M. Elton
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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 lambda_n(H+V)=lambda_n(H)+W(sqrt n)n^{-1/4}+O(n^{-1/2}ln(n)) as nto+infty, where W is a quasi-periodic function which can be defined explicitly in terms of V.
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