Three-Particle Problem with Pairwise Interactions Inversely Proportional to Squared Distance

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.