Application of the N-quantum approximation method to bound-state problems. I

The N-quantum approximation (NQA) is examined in the light of its application to the bound state of two scalar particle with scalar exchange. Bound-state wave functions are obtained as expansion coefficients in a truncated Haag expansion. An integral equation satisfied by the wave function is derived from the equations of motion for the Heisenberg fields and the NQA expansions. In the nonrelativistic limit the equation is shown to properly reduce to the Schroedinger equation. The equation is simplified by two different methods and then solved numerically. The results are compared with other calculations