  In this paper we build the relationship between smoothness of the functions
and convergence rate along curves for a class of generalized Schr\"{o}dinger
operators with polynomial growth. We show that the convergence rate depends
only on the growth condition of the phase function and regularity of the curve.
Our result can be applied to a wide class of operators. In particular,
convergence results along curves for a class of generalized Schr\"{o}dinger
operators with non-homogeneous phase functions is built and then the
convergence rate is established.
