Geodesic
On a~rapidly converging perturbation theory for a discrete spectrum
Teoretičeskaâ i matematičeskaâ fizika, Tome 24 (1975) no. 2, pp. 230-235

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The perturbation theory for the discrete spectrum of the radial Schrödinger equation is generalized to the case when nonperturbated function has knots. To the $k$-ih order the eigenfunction is calculated to the accuracy $\varepsilon^{2^k}$, where $\varepsilon$ is the perturbation parameter. It is possible to obtain from this eigenfunction the energy to the accuracy $\varepsilon^{2^{k+1}}$. All corrections are the quadratures of this function. The dependence on all other parts of spectrum is absent. The expressions for shiftings of the knots under the perturbation are obtained. 
@article{TMF_1975_24_2_a8,
     author = {V. S. Polikanov},
     title = {On a~rapidly converging perturbation theory for a discrete spectrum},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {230--235},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1975_24_2_a8/}
}
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V. S. Polikanov. On a~rapidly converging perturbation theory for a discrete spectrum. Teoretičeskaâ i matematičeskaâ fizika, Tome 24 (1975) no. 2, pp. 230-235. http://geodesic.mathdoc.fr/item/TMF_1975_24_2_a8/