  By their very nature, field-theoretical Hamiltonians are derived in momentum
representation. To solve the corresponding integro-differential equations is
more difficult than to solve the simpler differential equations in
configuration space (`Schr\"odinger equation'). For the latter many different
and very effective methods have been developed in the past. But rather than to
Fourier-transform to configuration space - which is not always easy - the
equations are solved here directly in momentum space, by using Gaussian
quadratures. Special attention is given to the case where the potential in
configuration space is linear and where the corresponding momentum-space kernel
has an almost intractable 1/(\vec k - \vec k')^4 -singularity. Its
regularization requires a certain technical effort, introducing suitable
counter terms. The method is numerically reliable and fast, faster than other
methods in the literature. It should be useful to and also applicable in other
approaches, including phenomenological Schr\"odinger-type equations.
