Geodesic
The asymptotics of spectral data of the harmonic oscillator perturbed by a~potential
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 31, Tome 303 (2003), pp. 223-271

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The asymptotics of spectral data of the perturbed harmonic oscillator $-y''+x^2y+q(x)y$ are obtained for the potentials $q(x)$ such that $q',xq\in L^2(\mathbb R)$. These results are important for the solution of the corresponding inverse spectral problem. 
@article{ZNSL_2003_303_a12,
     author = {D. S. Chelkak},
     title = {The asymptotics of spectral data of the harmonic oscillator perturbed by a~potential},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {223--271},
     publisher = {mathdoc},
     volume = {303},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_303_a12/}
}
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D. S. Chelkak. The asymptotics of spectral data of the harmonic oscillator perturbed by a~potential. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 31, Tome 303 (2003), pp. 223-271. http://geodesic.mathdoc.fr/item/ZNSL_2003_303_a12/