(Received August 30, 1968)
We introduce a new kind of coordinates to solve Schrodinger equation for the nonrelativistic three-body bound-state problem. With these coordinates, the boundary conditions are simplified, especially for the cases in which the three particles are in the equilateral position and in which they are in the in-line position. Further we replace the actual potential by a certain average of the potential, which still depends on one variable. Then the wave function can be separated into two parts: one which depends on a single variable and the other which is independent of the potential energy. The equation satisfied by the former wave function is reduced to the Morpurgo equation in the case of the ground state. The approximation can be improved with the aid of the perturbation theory, because our equations have been derived without recourse to the variational calculation.
URL : http://ptp.ipap.jp/link?PTPS/E68/80/
DOI : 10.1143/PTPS.E68.80