At the seminar, a quantum-mechanical problem of a pair of identical particles interacting with a third particle via zero-range interactions was discussed. A complete description was given to a system of two identical fermions (bosons) and a third particle. Correct formulation of the problem was presented, and bound-state energies were calculated for various total angular momenta. 

For this purpose, the generalized Coulomb problem was analyzed and its correspondence to the three-body problem was used to introduce the boundary condition in the vicinity of the triple-collision point. The related mathematical aspects and remaining obscure points were discussed.

Exact diffractionless solutions were obtained for the system of two-component one-dimensional particles with zero-range interactions. A new three-body bound state of odd parity was found, and the region of the parameters for which it exists was identified. One of the boundaries of this region is exactly determined by a diffractionless solution.

(Related to the election to the position of a senior researcher.)

Presentation