Geodesic
Construction of regular solutions of Schr\"odinger and Faddeev
Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 3, pp. 415-438

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We study the six-dimensional Schrödinger and Faddeev equations for a three-particle system with central pairwise interactions more general than the Coulomb interactions. The regular general and particular physical solutions of such equations are represented by infinite series in integer powers of the distance from one of the particles to the center of mass of the other two particles and in some functions of the other three-particle coordinates. Constructing such functions in the angular bases formed by spherical and bispherical harmonics or by symmetrized Wigner $D$-functions reduces to solving simple algebraic recurrence relations. For the projections of physical solutions on the angular basis functions, we introduce the boundary conditions in the linear three-particle configuration limit.
Keywords: three-particle problem, differential Schrödinger equation, differential Faddeev equation, regular solution, linear three-particle configuration. 
@article{TMF_2008_155_3_a2,
     author = {V. V. Pupyshev},
     title = {Construction of regular solutions of {Schr\"odinger} and {Faddeev}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {415--438},
     publisher = {mathdoc},
     volume = {155},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_155_3_a2/}
}
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V. V. Pupyshev. Construction of regular solutions of Schr\"odinger and Faddeev. Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 3, pp. 415-438. http://geodesic.mathdoc.fr/item/TMF_2008_155_3_a2/