The simultaneous integral equations of the vacuum expectation values in the Heisenberg representation are proposed, by the aid of which we reduced the equations to gain the expectation values, the S-matrix and the bound state solutions. The relation of these equations with the methods of Dyson, Bethe-Salpeter and Tomonaga is obvious. The practical calculations are carried out for the system containing one Fermion and the neutral scalar mesons. The application to other general systems may be readily possible.