On the Bound State of three Particles



The expansion of the function Ψ of three particles interacting with each other via the potentials V12; V13; V23 in a complete set of the functions describing the motion of two particles coupled by a finite potential well V12 (the complex particle) is considered. It is shown that in this expansion the population of the highest virtual states decreases with energy as equation image. The system of integral differential equations for the bound state of three particles can be cut off (all the ϕn in (9) with ϵn > ϵs, where ϵs is rather large, may be neglected).