Asymptotic inverse problem for almost-periodically perturbed quantum harmonic oscillator

被引:0
|
作者
Pokrovski, Alexis [1 ]
机构
[1] St Petersburg State Univ, Lab Quantum Networks, Inst Phys, St Petersburg 198504, Russia
关键词
almost-periodic perturbation; inverse problem; quantum harmonic oscillator; spectral asymptotics;
D O I
10.1007/s11040-007-9025-4
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let {mu(n)}(n=0)(infinity) be the spectrum of -d(2/)dx(2) + x(2) + q( x) in L-2( R), where q is an even almost-periodic complex-valued function with bounded primitive and derivative. It is known that mu(n) = mu(0)(n) + O(n(-1/4)), where {mu(0)(n)}(n=0)(infinity) is the spectrum of the unperturbed operator. Suppose that the asymptotic approximation to the first asymptotic correction Delta mu(n) = mu n - mu(0)(n)+ o( n(-1/4)) is given. We prove the formula that recovers the frequencies and the Fourier coefficients of q in terms of Delta mu(n).
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页码:197 / 203
页数:7
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