Geodesic
Wave operators and positive eigenvalues for a Schrödinger equation with oscillating potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 15 (1973) no. 3, pp. 353-366 Cet article a éte moissonné depuis la source Math-Net.Ru

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A study is made of the Schrödinger equation on a half,axis with a potential $q(x)$ that is not absolutely integrable and may be unbounded at infinity. The main result of the paper is the proof of the existence and completeness of the wave operators $W_{\pm}(H,H_0)$ under the condition that the Fourier transform of the potential at the upper limit converges sufficiently fast everywhere except at a certain discrete set of points $k_j$. It is also proved that for such potentials eigenvalues in the continuous spectrum can appear only at the points $\lambda_j=k_j^2/4$. 
@article{TMF_1973_15_3_a7,
     author = {V. B. Matveev},
     title = {Wave operators and positive eigenvalues for a {Schr\"odinger} equation with oscillating potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {353--366},
     year = {1973},
     volume = {15},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1973_15_3_a7/}
}
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V. B. Matveev. Wave operators and positive eigenvalues for a Schrödinger equation with oscillating potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 15 (1973) no. 3, pp. 353-366. http://geodesic.mathdoc.fr/item/TMF_1973_15_3_a7/

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