Asymptotic Inverse Problem for Almost-Periodically Perturbed Quantum Harmonic Oscillator

Details Asymptotic Inverse Problem for Almost-Periodically Perturbed Quantum Harmonic Oscillator Asymptotic Inverse Problem for Almost-Periodically Perturbed Quantum Harmonic Oscillator

2006-01-08

arxiv.org/abs/math-ph/0601014v1

Physics

Mathematical Physics

6 pages

Scientific paper

10.1007/s11040-007-9025-4

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 $\{\Delta\mu_n\}_{n=0}^\infty$ ($\Delta\mu_n=\mu_n-\mu_n^0+o(n^{-1/4})$, where $\mu_n^0$ and $\mu_n$ 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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