  When a nonrelativistic particle interacts with a scalar quantum field, the
standard perturbation theory leads to a dependence of the energy of its ground
state on an undefined parameter---"momentum cutoff"---due to the ultraviolet
divergence. We show that the use of nonasymptotic states of the system results
in a calculation scheme in which all observable quantities remain finite and
continuously depend on the coupling constant without any additional parameters.
It is furthermore demonstrated that the divergence of traditional perturbation
series is caused by the energy being a function with a logarithmic singularity
for small values of the coupling constant.
