Asymptotics of spectral data of a harmonic oscillator perturbed by a potential
The author proves some results on the asymptotic behaviour of the eigenvalues, and the normalizing constants of the corresponding eigenfunctions, of the perturbed harmonic oscillator \[ -y''(x)+x^{2}y(x)+q(x)y(x), \] where \(q'(x)\), \(xq(x)\in L^{2}(\mathbb R)\). As shown by the author, \textit{P. Kargaev} and \textit{E. Korotyaev} [Commun. Math. Phys. 249, No.~1, 133--196 (2004; Zbl 1085.81055)], these results are important for solving the corresponding inverse spectral problem.
scientific article; zbMATH DE number 5312814