Geodesic
On the possibility of expanding the Sohr\"odinger equation solution witn regard to the solutions of potential scattering problem
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 10, Tome 89 (1979), pp. 204-209

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The paper deals with Sohrödinger equation with Povzner potential function defined on the three-dimensional space. The requirements have been found which are necessary for presentting the solution in the form $u(x)=\int_{|\alpha|=1}\Psi(x,\alpha)\,d\mu_\alpha$, $\Psi(x,\alpha)$ being the solution of the potential scattering problem. These requirements have been demonstrated to be as well sufficient if certain stricter limitations are imposed on the potential function. 
@article{ZNSL_1979_89_a13,
     author = {E. G. Maltzeva and D. M. \`Eidus},
     title = {On the possibility of expanding the {Sohr\"odinger} equation solution witn regard to the solutions of potential scattering problem},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {204--209},
     publisher = {mathdoc},
     volume = {89},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_89_a13/}
}
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E. G. Maltzeva; D. M. Èidus. On the possibility of expanding the Sohr\"odinger equation solution witn regard to the solutions of potential scattering problem. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 10, Tome 89 (1979), pp. 204-209. http://geodesic.mathdoc.fr/item/ZNSL_1979_89_a13/