  The phenomenology of the pseudo scalar mesons D_s and B_s and of the vector
mesons D_s* and B_s* was investigated in simulations of quenched lattice QCD.
The work is particularly focused on the continuum limit and the minimisation of
all systematic errors within the quenched approximation. The decay constants
F_Ds and F_Ds* and the difference in the masses between the D_s and the D_s*
were determined from the direct computer simulation of lattice QCD in large
physical volume (L ~ 1.5 fm). As an aside, the renormalisation group invariant
charm quark mass M_c could be obtained from the simulation results. For the
B_s- and the B_s*-meson, an interpolation in the meson mass to its physical
point was carried out for the decay constant and the mass splitting in the
continuum limit. The functional form of the interpolation to the static limit
was guided by the prediction of the Heavy Quark Effective Theory (HQET). A set
of conversion functions between HQET and QCD were derived and evaluated
numerically with input from perturbation theory.
