Schr\"{o}dinger equation for one-dimensional ground state or first
excited state of three particles of an equal mass is assumed
re-arrangeable as a separable differential bound-state problem.
Starting from an elementary ``suitable" ansatz for the (= single!)
wave function, one enters the well known terrain allowing to
deduce the original form and parameters of the (two- plus
three-body) interactions V. Three explicit examples (with
V=polynomial, singular or PT-symmetric) are presented. The
first-order perturbation results are added, tabulated and
numerically cross-checked.



MR2317509 Chafa, F.; Chouchaoui, A.; Hachemane, M.; Ighezou, F. Z.
The quasi-exactly solvable potentials method applied to the
three-body problem. Ann. Physics 322 (2007), no. 5, 1034--1042.
81U15