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Asymptotic Inverse Problem for Almost-Periodically Perturbed Quantum Harmonic Oscillator

Alexis Pokrovski
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Abstract

Consider quantum harmonic oscillator, perturbed by an even almost-periodic complex-valued potential with bounded derivative and primitive. Suppose that we know the first correction to the spectral asymptotics $\{Δμ_n\}_{n=0}^\infty$ ($Δμ_n=μ_n-μ_n^0+o(n^{-1/4})$, where $μ_n^0$ and $μ_n$ is the spectrum of the unperturbed and the perturbed operators, respectively). We obtain the formula that recovers the frequencies and the Fourier coefficients of the perturbation.

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Alexis Pokrovski. 2006-01-08. Asymptotic Inverse Problem for Almost-Periodically Perturbed Quantum Harmonic Oscillator. https://doi.org/10.1007/s11040-007-9025-4

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