On the Bound State of three Particles

The expansion of the function Ψ of three particles interacting with each other via the potentials V 12 ; V 13 ; V 23 in a complete set of the functions describing the motion of two particles coupled by a finite potential well V 12 (the complex particle) is considered. It is shown that in this expansion the population of the highest virtual states decreases with energy as \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{\varepsilon }{{\mathop \varepsilon \nolimits_n^3 }} $\end{document} . The system of integral differential equations for the bound state of three particles can be cut off (all the ϕ n in (9) with ϵ n > ϵ s , where ϵ s is rather large, may be neglected).