The Bethe-Salpeter (BS) equation in the ladder approximation is studied within a scalar theory: two scalar fields (constituents) with mass
m interacting via an exchange of a scalar field (tieon) with mass
. The BS equation is written in the form of an integral equation in the configuration Euclidean
x-space with the kernel which for stable bound states
M < 2
m is a self-adjoint positive operator. The solution of the BS equation is formulated as a variational problem. The nonrelativistic limit of the BS equation is considered. The role of so-called abnormal states is discussed.
The analytical form of test functions for which the accuracy of calculations of bound-state masses is better than 1% (the comparison with available numerical calculations is done) is determined. These test functions make it possible to calculate analytically vertex functions describing the interaction of bound states with constituents.
As a by-product a simple solution of the Wick-Cutkosky model for the case of massless bound states is demonstrated.