Geodesic
Three-Particle Problem with Pairwise Interactions Inversely Proportional to Squared Distance
Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 2, pp. 268-287

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The hyperharmonic method is used to investigate the three-particle Schrödinger and Faddeev equations with pairwise interactions inversely proportional to the squared distance. Exact solutions for such equations are constructed in the form of a product of the Bessel function depending on the hyperradius and a finite linear combination of the hyperharmonics. A criterion for the existence of such solutions is proved and analyzed. 
@article{TMF_2001_128_2_a8,
     author = {V. V. Pupyshev},
     title = {Three-Particle {Problem} with {Pairwise} {Interactions} {Inversely} {Proportional} to {Squared} {Distance}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {268--287},
     publisher = {mathdoc},
     volume = {128},
     number = {2},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_128_2_a8/}
}
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V. V. Pupyshev. Three-Particle Problem with Pairwise Interactions Inversely Proportional to Squared Distance. Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 2, pp. 268-287. http://geodesic.mathdoc.fr/item/TMF_2001_128_2_a8/