  This research is concerned with the inter-particle potentials for
few-particle bound state systems in a scalar model with a Higgs-like mediating
field and QCD. The variational method, in a reformulated Hamiltonian formalism
of QFT, is used to derive relativistic few particle wave equations and,
consequently, the corresponding inter-particle potentials for stationary states
of systems in question. The cubic and quartic contributions to the
inter-particle potentials, in the non-relativistic limit, are expressed as
multi-dimensional integrals. In the scalar Higgs-like model, when the mediator
is massive, it is found that the non-linear terms modify the attractive Yukawa
potential. In the case of QCD, the derived quark-antiquark potential is
significantly affected by the non-linear terms and provides a signal of
confinement.
