  We first give the solution for the local approximation of a four parameter
family of generalized one-dimensional point interactions within the framework
of non-relativistic model with three neighboring $\delta$ functions. We also
discuss the problem within relativistic (Dirac) framework and give the solution
for a three parameter family. It gives a physical interpretation for so-called
$\epsilon$ potential. It will be also shown that the scattering properties at
high energy substantially differ between non-relativistic and relativistic
cases.
