three particles. The corresponding eigenvectors have been used to compute the second order estimate of the tangent of the phase-shift. In order to show the results in a visible way, we compute the effective range function K ( E $^{0}$) using the PHH method, which gives an almost exact result. Then, the second order estimates obtained from the bound state like wave functions have been compared to K ( E $^{0}$). We have observed that the variational estimates and the exact results at the level of four digits coincide. This is practically the level of accuracy reached by the PHH method, therefore we can conclude that the results based on the integral relations can reach the same level of accuracy as other methods usually used to describe scattering states in A = 3. Moreover, a similar accuracy has been obtained when the Coulomb interaction has been considered. We consider this result to be of particular importance. For example, the application of the Faddeev method for describing p − d scattering has been a subject of intense investigations and different techniques for including the long range Coulomb interaction has been proposed (see the Introduction). From the results presented here it emerges that elastic p − d scattering in the low energy region can be described using bound state like wave functions which can be easily computed. Furthermore, we have also analyzed the computation of p − d phase-shifts from a calculation in which the Coulomb potential has been screened, as we have done in the two-nucleon system. Again, for suitable values of r$_{sc}$ and n we were able to reproduce the p − d phase-shifts using the integral relations. This result will be useful for a simple extension of the Faddeev method, normally used to describe n − d scattering, to determine p − d phases without the normalization procedure described in Ref. [20]. In the last Section we discuss an application of the integral relations in connection with the HA method. This method is often used to describe three-body bound states in nuclear, atomic and molecular physics. It is very efficient, in particular when the interaction has a strong repulsion at short distances. In Ref. [22] we have shown how to apply the HA method to describe a 1+2 collision solving the system of Eq. (51) with appropriate boundary conditions and then, using the integral relations, the phase shift has been extracted. Here we have shown a different application, the system of equations given in Eq. (51) has been solved using bound state boundary conditions and then, using the integral relations, the phase shift has been extracted. We have solved the same case previously considered using the PHH expansion for the J = 3 / 2 $^{+}$, T = 1 / 2 state. We have obtained an extremely good description of the phase-shifts using HA bound state like wave functions. This application 22