Geodesic
Description of the pair potentials for which the scattering in the quantum system of three one-dimensional particles
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 11, Tome 84 (1979), pp. 16-22

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The coordinate asymptotics of a solution of the scatterinq problem in the quantum system of three one-dimensional particles contains besides plane and spherical waves the diffraction waves, which also occur in the two-dimensional problem of diffraction of the plane wave on the semi-infinite screen. The class of potentials is found for which there are no diffraction waves in the asymptotics of the solution. This class is somewhat wider then well-known Bargmann class. 
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     author = {V. S. Buslaev and S. P. Merkur'ev and S. P. Salikov},
     title = {Description of the pair potentials for which the scattering in the quantum system of three one-dimensional particles},
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     publisher = {mathdoc},
     volume = {84},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_84_a2/}
}
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V. S. Buslaev; S. P. Merkur'ev; S. P. Salikov. Description of the pair potentials for which the scattering in the quantum system of three one-dimensional particles. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 11, Tome 84 (1979), pp. 16-22. http://geodesic.mathdoc.fr/item/ZNSL_1979_84_a2/