Geodesic
A perturbed boundary eigenvalue problem for the Schrödinger operator on an interval
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 4, pp. 679-698 
I. Kh. Khusnullin. A perturbed boundary eigenvalue problem for the Schrödinger operator on an interval. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 4, pp. 679-698. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_4_a6/
@article{ZVMMF_2010_50_4_a6,
     author = {I. Kh. Khusnullin},
     title = {A perturbed boundary eigenvalue problem for the {Schr\"odinger} operator on an interval},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {679--698},
     year = {2010},
     volume = {50},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_4_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A perturbed two-parameter boundary value problem is considered for a second-order differential operator on an interval with Dirichlet conditions. The perturbation is described by the potential $\mu^{-1}V((x-x_0)\varepsilon^{-1})$, where $0<\varepsilon\ll1$ and $\mu$ is an arbitrary parameter such that there exists $\delta>0$ for which $\varepsilon/\mu=o(\varepsilon^\delta)$. It is shown that the eigenvalues of this operator converge, as $\varepsilon\to0$, to the eigenvalues of the operator with no potential. Complete asymptotic expansions of the eigenvalues and eigenfunctions of the perturbed operator are constructed.

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