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 TMF, 1973, Volume 15, Number 3, Pages 353–366 (Mi tmf3675)

Wave operators and positive eigenvalues for a Schrödinger equation with oscillating potential

V. B. Matveev

Abstract: 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 $\lambda_j=k_j^2/4$.

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English version:
Theoretical and Mathematical Physics, 1973, 15:3, 574–583

Citation: V. B. Matveev, “Wave operators and positive eigenvalues for a Schrödinger equation with oscillating potential”, TMF, 15:3 (1973), 353–366; Theoret. and Math. Phys., 15:3 (1973), 574–583

Citation in format AMSBIB
\Bibitem{Mat73} \by V.~B.~Matveev \paper Wave operators and positive eigenvalues for a Schr\"odinger equation with oscillating potential \jour TMF \yr 1973 \vol 15 \issue 3 \pages 353--366 \mathnet{http://mi.mathnet.ru/tmf3675} \transl \jour Theoret. and Math. Phys. \yr 1973 \vol 15 \issue 3 \pages 574--583 \crossref{https://doi.org/10.1007/BF01094564} 

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This publication is cited in the following articles:
1. A. B. Khasanov, “Eigenvalues of the Dirac operator in the continuous spectrum”, Theoret. and Math. Phys., 99:1 (1994), 396–401
2. S. N. Naboko, A. B. Pushnitskii, “Point Spectrum on a Continuous Spectrum for Weakly Perturbed Stark Type Operators”, Funct. Anal. Appl., 29:4 (1995), 248–257
3. V. B. Matveev, “Positons: Slowly Decreasing Analogues of Solitons”, Theoret. and Math. Phys., 131:1 (2002), 483–497
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