  It is shown that the momentum-dependent kaon-antikaon interactions generated
via vector meson exchange from the standard SU_V(3) x SU_A(3) interaction
Lagrangian lead to a non-local potential in coordinate space that can be
incorporated without approximation into a non-relativistic version of the
Bethe-Salpeter wave equation containing a radial-dependent effective kaon mass
appearing in a fully symmetrized kinetic energy operator, in addition to a
local potential. Estimates of the mass and decay widths of f_0(980) and
a_0(980), considered as KKbar molecules of isospin 0 and 1, as well as for
K^+K^- atomic bound states (kaonium) are presented, and compared with previous
studies of a similar nature. It is argued that without a better knowledge of
hadronic form factors it is not possible to distinguish between the molecular
versus elementary particle models for the structure of the light scalar mesons.
