Wave operators and positive eigenvalues for a Schr\"odinger equation with oscillating potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 15 (1973) no. 3, pp. 353-366
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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},
publisher = {mathdoc},
volume = {15},
number = {3},
year = {1973},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1973_15_3_a7/}
}
TY - JOUR AU - V. B. Matveev TI - Wave operators and positive eigenvalues for a Schr\"odinger equation with oscillating potential JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1973 SP - 353 EP - 366 VL - 15 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1973_15_3_a7/ LA - ru ID - TMF_1973_15_3_a7 ER -
V. B. Matveev. Wave operators and positive eigenvalues for a Schr\"odinger 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/