COMMON EIGENKETS OF 3-PARTICLE COMPATIBLE OBSERVABLES

We give common eigenkets of three compatible observables {P-1+P-2+P-3, (mu(2)Q(2)+mu(3)Q(3))/(mu(2)+mu(3)) -Q(1), Q(3)-Q(2)}, which are comp osed of three particles' coordinate Q(i) and momentum P-i, where mu(i) =m(i)/(m(1)+m(2)+m(3)). This set of operators are so-called Jacobi coo rdinates and momenta. By compatible we mean such observables can be si multaneously determined. Using the technique of integration within an ordered product of operators, we prove that the common eigenkets are c omplete and orthonormal, and hereby qualified for making up a represen tation. Applying this representation to solving some new three-body pr oblems is also shown.