Geodesic
On scattering of the Schr\"odinger operator with non-local potential
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 29 (2004) no. 1, pp. 109-124

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We consider the Schrödinger operator of the form $H=$ $=-d^2/dx^2+V$ acting in $L^2(R)$ where $V=\varepsilon W(x)+\lambda (\cdot ,\varphi _0)\varphi _0$ is non-local potential and $W(x),\, \varphi _0(x)$ are decreasing functions for $|x| \to \infty$. The existence and completeness of the wave operators is proved. We investigate the asymptotic behaviour of solutions of the Lippmann–Schwinger equation and study the scattering amplitude. 
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     author = {M. S. Smetanina},
     title = {On scattering of the {Schr\"odinger} operator with non-local potential},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {109--124},
     publisher = {mathdoc},
     volume = {29},
     number = {1},
     year = {2004},
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     url = {http://geodesic.mathdoc.fr/item/IIMI_2004_29_1_a5/}
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M. S. Smetanina. On scattering of the Schr\"odinger operator with non-local potential. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 29 (2004) no. 1, pp. 109-124. http://geodesic.mathdoc.fr/item/IIMI_2004_29_1_a5/